library(readr)
## Warning: package 'readr' was built under R version 4.2.2
train <- read_csv("C:/Users/vidhi/Downloads/train.csv")
## Rows: 891 Columns: 11
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (4): Name, Sex, Ticket, Embarked
## dbl (7): PassengerId, Survived, Pclass, Age, SibSp, Parch, Fare
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
View(train)
str(train)
## spc_tbl_ [891 × 11] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
##  $ PassengerId: num [1:891] 1 2 3 4 5 6 7 8 9 10 ...
##  $ Survived   : num [1:891] 0 1 1 1 0 0 0 0 1 1 ...
##  $ Pclass     : num [1:891] 3 1 3 1 3 3 1 3 3 2 ...
##  $ Name       : chr [1:891] "Braund, Mr. Owen Harris" "Cumings, Mrs. John Bradley (Florence Briggs Thayer)" "Heikkinen, Miss. Laina" "Futrelle, Mrs. Jacques Heath (Lily May Peel)" ...
##  $ Sex        : chr [1:891] "male" "female" "female" "female" ...
##  $ Age        : num [1:891] 22 38 26 35 35 NA 54 2 27 14 ...
##  $ SibSp      : num [1:891] 1 1 0 1 0 0 0 3 0 1 ...
##  $ Parch      : num [1:891] 0 0 0 0 0 0 0 1 2 0 ...
##  $ Ticket     : chr [1:891] "A/5 21171" "PC 17599" "STON/O2. 3101282" "113803" ...
##  $ Fare       : num [1:891] 7.25 71.28 7.92 53.1 8.05 ...
##  $ Embarked   : chr [1:891] "S" "C" "S" "S" ...
##  - attr(*, "spec")=
##   .. cols(
##   ..   PassengerId = col_double(),
##   ..   Survived = col_double(),
##   ..   Pclass = col_double(),
##   ..   Name = col_character(),
##   ..   Sex = col_character(),
##   ..   Age = col_double(),
##   ..   SibSp = col_double(),
##   ..   Parch = col_double(),
##   ..   Ticket = col_character(),
##   ..   Fare = col_double(),
##   ..   Embarked = col_character()
##   .. )
##  - attr(*, "problems")=<externalptr>
attach(train)
#Get the Correlations between the measurements

Temp2=train[,-c(1,3,4,7,8,9)]
Temp2=na.omit(Temp2)
Temp2$Sex<-as.numeric(factor(Temp2$Sex, levels = unique(Temp2$Sex)))

Temp2$Embarked<-as.numeric(factor(Temp2$Embarked, labels=c("1","2","3")))

cor(Temp2[-1])
##                  Sex         Age        Fare    Embarked
## Sex       1.00000000 -0.09903723  0.18245683 -0.10963900
## Age      -0.09903723  1.00000000  0.09314252 -0.03256492
## Fare      0.18245683  0.09314252  1.00000000 -0.28351044
## Embarked -0.10963900 -0.03256492 -0.28351044  1.00000000
# Using prcomp to compute the principal components (eigenvalues and eigenvectors). With scale=TRUE, variable means are set to zero, and variances set to one
Temp2_pca <- prcomp(Temp2[,-1],scale=TRUE)
Temp2_pca
## Standard deviations (1, .., p=4):
## [1] 1.1816256 1.0408997 0.9141950 0.8273671
## 
## Rotation (n x k) = (4 x 4):
##                  PC1        PC2        PC3        PC4
## Sex       0.44571001 -0.5293273 0.64187639  0.3303784
## Age       0.09242234  0.8292140 0.48163361  0.2681255
## Fare      0.65697225  0.1418393 0.04129893 -0.7392993
## Embarked -0.60098933 -0.1099922 0.59524631 -0.5219151
summary(Temp2_pca)
## Importance of components:
##                           PC1    PC2    PC3    PC4
## Standard deviation     1.1816 1.0409 0.9142 0.8274
## Proportion of Variance 0.3491 0.2709 0.2089 0.1711
## Cumulative Proportion  0.3491 0.6199 0.8289 1.0000
# sample scores stored in Temp2_pca$x
# singular values (square roots of eigenvalues) stored in sparrow_pca$sdev
# loadings (eigenvectors) are stored in Temp2_pca$rotation
# variable means stored in Temp2_pca$center
# variable standard deviations stored in Temp2_pca$scale
# A table containing eigenvalues and %'s accounted, follows
# Eigenvalues are sdev^2
(eigen_Temp2 <- Temp2_pca$sdev^2)
## [1] 1.3962390 1.0834721 0.8357525 0.6845364
names(eigen_Temp2) <- paste("PC",1:4,sep="")
eigen_Temp2
##       PC1       PC2       PC3       PC4 
## 1.3962390 1.0834721 0.8357525 0.6845364
sumlambdas <- sum(eigen_Temp2)
sumlambdas
## [1] 4
propvar <- eigen_Temp2/sumlambdas
propvar
##       PC1       PC2       PC3       PC4 
## 0.3490598 0.2708680 0.2089381 0.1711341
cumvar_Temp2 <- cumsum(propvar)
cumvar_Temp2
##       PC1       PC2       PC3       PC4 
## 0.3490598 0.6199278 0.8288659 1.0000000
matlambdas <- rbind(eigen_Temp2,propvar,cumvar_Temp2)
rownames(matlambdas) <- c("Eigenvalues","Prop. variance","Cum. prop. variance")
round(matlambdas,4)
##                        PC1    PC2    PC3    PC4
## Eigenvalues         1.3962 1.0835 0.8358 0.6845
## Prop. variance      0.3491 0.2709 0.2089 0.1711
## Cum. prop. variance 0.3491 0.6199 0.8289 1.0000
summary(Temp2_pca)
## Importance of components:
##                           PC1    PC2    PC3    PC4
## Standard deviation     1.1816 1.0409 0.9142 0.8274
## Proportion of Variance 0.3491 0.2709 0.2089 0.1711
## Cumulative Proportion  0.3491 0.6199 0.8289 1.0000
Temp2_pca$rotation
##                  PC1        PC2        PC3        PC4
## Sex       0.44571001 -0.5293273 0.64187639  0.3303784
## Age       0.09242234  0.8292140 0.48163361  0.2681255
## Fare      0.65697225  0.1418393 0.04129893 -0.7392993
## Embarked -0.60098933 -0.1099922 0.59524631 -0.5219151
print(Temp2_pca)
## Standard deviations (1, .., p=4):
## [1] 1.1816256 1.0408997 0.9141950 0.8273671
## 
## Rotation (n x k) = (4 x 4):
##                  PC1        PC2        PC3        PC4
## Sex       0.44571001 -0.5293273 0.64187639  0.3303784
## Age       0.09242234  0.8292140 0.48163361  0.2681255
## Fare      0.65697225  0.1418393 0.04129893 -0.7392993
## Embarked -0.60098933 -0.1099922 0.59524631 -0.5219151
## Sample scores stored in sparrow_pca$x
Temp2_pca$x
##                 PC1           PC2           PC3          PC4
##   [1,] -1.036571945 -0.1675817029 -0.4512155112 -0.280517248
##   [2,]  2.328844131  0.1022918285 -0.0644045317  1.147406212
##   [3,] -0.076863406 -1.0364253330  1.0155382614  0.470315955
##   [4,]  0.541154997 -0.4004517724  1.3498713191  0.005941459
##   [5,] -0.943742080  0.5783575367 -0.0185714058 -0.051183852
##   [6,] -0.278861772  1.7828311382  0.6470218066 -0.311526470
##   [7,] -0.992543997 -1.2748413981 -1.1050763987 -0.843594832
##   [8,] -0.030671121 -0.9706142289  1.0512734542  0.444011801
##   [9,]  1.664344689 -1.3812908595 -0.8941309506  1.278937145
##  [10,] -0.108260428 -2.2716456857  0.2912731112 -0.059238176
##  [11,]  0.358340114  0.8443588327  2.0935020004  0.802227620
##  [12,] -1.039398015 -0.2798683728 -0.5170560246 -0.328690272
##  [13,] -0.630009991  0.8694448494  0.1324763008 -0.301524135
##  [14,] -0.154266787 -1.7231957561  0.6166953333  0.249299556
##  [15,]  0.208282705  0.6444468869  1.9855747253  0.894059299
##  [16,] -0.121191971 -1.1120830961 -1.8628754064 -0.286066237
##  [17,]  0.080053345 -0.7233559402  1.1895595915  0.422118607
##  [18,] -0.720981351  0.6264512250 -0.0045681066 -0.301859366
##  [19,] -0.888689303  0.5344050809 -0.0479420797 -0.138812068
##  [20,]  0.625733012 -1.5243219921 -0.1140148752  0.935304605
##  [21,] -0.647725138  0.2513992845 -0.2297830451 -0.564031854
##  [22,] -0.028458129 -2.0310634439  0.4276154032 -0.046334256
##  [23,]  0.290832573 -0.2869811981  1.4326297117  0.364662359
##  [24,]  2.118171868  0.3460076983 -0.3513946758 -3.907620912
##  [25,]  0.875161156  1.1995167387 -1.3652222002  1.106508508
##  [26,] -0.715648479  2.3585887361  1.0135414535  0.488114652
##  [27,]  1.474364633  0.6588246642 -1.7215319207  0.124097704
##  [28,] -0.353680136  1.0966188162  0.2483413792 -0.535451822
##  [29,] -1.033020953 -0.2226533122 -0.4838237166 -0.310189844
##  [30,] -0.002848466 -1.4671517284  0.7575395885  0.181613043
##  [31,]  1.430674269 -1.4317399327 -0.9088200604  1.541889474
##  [32,]  0.031651073 -0.2312615472  1.4819997708  0.707675872
##  [33,]  0.091775301 -0.9441782404  1.0589707441  0.306221266
##  [34,]  1.737017034 -1.9798219080 -1.2507083116  0.914715217
##  [35,]  0.649379751 -1.2958636466  0.0187973373  1.011401099
##  [36,] -0.005330479 -1.4676875913  0.7573835629  0.184406085
##  [37,] -0.729676286 -0.9388973610 -0.9243947250 -1.011020158
##  [38,] -1.036123470 -0.2233231407 -0.4840187487 -0.306698542
##  [39,]  2.466575808  0.7462487722  0.3053993550  1.274857785
##  [40,]  0.166579768 -0.8163515486  1.1293360004  0.273396074
##  [41,]  1.459736803  2.7216822690 -0.5076885621  1.090593468
##  [42,] -0.076792792 -1.3156014023  0.8513855516  0.341853400
##  [43,]  0.547522780  0.4866401084 -1.7633798140  1.179923077
##  [44,]  0.035247891 -2.1848242042  0.3331258345 -0.195053315
##  [45,] -0.614660418 -0.6907125655 -0.7858388195 -1.037742521
##  [46,]  0.506071875  0.1147422142 -1.9793898155  1.059670295
##  [47,]  0.056057955  1.3525954097  0.3725928346 -0.919505513
##  [48,] -0.895091155 -1.1421249580 -1.0332874086 -0.901906532
##  [49,] -0.025776293 -0.8578809172  1.1172440150  0.489856824
##  [50,] -1.044431067 -0.3367932638 -0.5502038446 -0.348703132
##  [51,] -0.134256967 -1.5513608787  0.7164474901  0.303812103
##  [52,] -0.993534474  0.0650630709 -0.3171843486 -0.226241395
##  [53,] -0.932468599  0.4132766744 -0.1163570157 -0.140899900
##  [54,]  0.343048387 -1.5041496720  0.7136206745 -0.258982373
##  [55,] -0.220781974 -0.0472922039 -0.4327643331 -1.224212819
##  [56,]  0.621242869  0.3629605012 -1.8408241584  1.032773366
##  [57,] -0.361657574  0.5365138702 -0.0804744001 -0.783240892
##  [58,] -1.012476731  0.0051352047 -0.3512065362 -0.230602048
##  [59,] -0.901655367 -1.3205494547 -1.1377756838 -0.975914620
##  [60,]  0.005110655 -0.7953742112  1.1520170759  0.480775963
##  [61,] -1.014854325 -0.1628929032 -0.4498502870 -0.304956365
##  [62,] -0.964009855  0.2389521784 -0.2168340676 -0.182435974
##  [63,] -0.503768344  0.2824793282 -0.2207335593 -0.726028287
##  [64,] -0.102301041 -1.5444616449  0.7184563199  0.267851688
##  [65,]  0.066125823 -0.6146863442  1.2543469319  0.489144664
##  [66,] -0.738211213 -0.4381956715 -0.6294483843 -0.770326129
##  [67,]  3.069503611 -0.5246444689  1.1148325103 -3.147361192
##  [68,] -1.013889766 -0.0510081303 -0.3841267929 -0.254688560
##  [69,] -0.982004454  0.2350671729 -0.2179652533 -0.162186420
##  [70,] -1.041827907 -0.2803929825 -0.5172087736 -0.325955884
##  [71,] -0.214309508  1.3500617657  0.3884282861 -0.589580909
##  [72,] -0.845699534  0.0969804002 -0.3078910727 -0.392601955
##  [73,] -0.800620638  1.9493755407  0.7783798817  0.403998588
##  [74,]  1.158894058  2.9917603749 -0.3296117147  1.583195391
##  [75,]  1.209014909  0.3223447643 -1.9023696200  0.294316071
##  [76,]  0.161234875 -0.5383141877  1.2931571557  0.407793843
##  [77,] -0.727358414  0.5692361643 -0.0378004145 -0.320359794
##  [78,] -0.064471655 -0.9220734477  1.0819800975  0.507724595
##  [79,] -0.173778840 -0.0371443017 -0.4298095980 -1.277106050
##  [80,] -0.948998041  0.4655462570 -0.0845646682 -0.096622488
##  [81,] -0.932539213  0.6924527437  0.0477956940 -0.012437345
##  [82,] -0.990295149  0.1774389620 -0.2513178570 -0.178533413
##  [83,] -0.112161487 -1.3232374475  0.8491621866  0.381654248
##  [84,] -0.926524525  0.7495895684  0.0810052222  0.006470867
##  [85,] -0.321794824  1.3826941194  0.4145029188 -0.442949682
##  [86,]  1.473730145 -1.3945251058 -0.8896977450  1.506276452
##  [87,] -1.026643890 -0.1654382516 -0.4505914087 -0.291689416
##  [88,] -0.091546650 -1.3746250000  0.8176266572  0.332779489
##  [89,]  1.489723682 -1.2514764691 -0.8066137767  1.552470265
##  [90,] -1.034572211 -0.2229882265 -0.4839212327 -0.308444193
##  [91,]  0.050371589  2.7498782185  0.3968624480  1.279719438
##  [92,] -0.821294068  0.2697642906 -0.2078625945 -0.343035886
##  [93,]  3.500861199  0.8729890093 -1.7254669726 -2.259051431
##  [94,]  0.059862195 -2.3470248039  0.2361788623 -0.299781963
##  [95,] -0.220781974 -0.0472922039 -0.4327643331 -1.224212819
##  [96,]  0.856496849  0.7767001720 -1.6126312086  0.934937055
##  [97,]  0.027568597 -0.6509299197  1.2355074129  0.519695298
##  [98,]  0.036664218  1.8509526994  0.6668565633 -0.666591926
##  [99,]  0.492096651 -0.4466576443 -2.3085826307  0.818630611
## [100,] -1.025161831 -0.0534417513 -0.3848353832 -0.242003960
## [101,] -0.893312280  1.1476278804  0.3129130357  0.148833028
## [102,]  0.584492113  0.7458939120 -1.6133143950  1.253865794
## [103,] -1.051808084 -0.2825476869 -0.5178361527 -0.314725062
## [104,]  0.138651104  0.1827074307  1.7185460698  0.767003689
## [105,]  0.166579768 -0.8163515486  1.1293360004  0.273396074
## [106,] -0.946082865  0.0194695352 -0.3470328509 -0.305315920
## [107,]  0.609453478  0.1929004015 -1.9400595584  0.969010264
## [108,]  0.106324917 -1.3877431053  0.7972339315  0.084435450
## [109,] -0.371914372  0.8134907585  0.0830379805 -0.643315693
## [110,] -1.050427438 -0.5056026596 -0.6490750808 -0.418985194
## [111,]  1.411988553  0.4220047153 -1.8567787569  0.091583837
## [112,] -0.104543417 -1.2657544555  0.8824725073  0.398758155
## [113,]  0.008732262 -1.1296218900  0.9552561607  0.322640812
## [114,] -0.290457192 -0.1993767184 -1.3153815378  0.340912606
## [115,] -1.009337404 -0.3850548604 -0.5808291985 -0.413871101
## [116,] -0.689606114 -0.2601871186 -0.5278986563 -0.747992218
## [117,] -0.997913218  0.1199559700 -0.2846281777 -0.195637320
## [118,]  0.142972844 -1.9382135057  0.4712234148 -0.213571117
## [119,] -0.711415758  0.7122738159  0.0452803553 -0.274108724
## [120,] -0.837672804  0.9921255660  0.2179163837  0.009191356
## [121,] -0.786174026  1.5057884376  0.5166365941  0.182328683
## [122,]  0.625789110 -1.1080768203  0.9283830454 -0.423094436
## [123,] -0.813012301  1.7512662798  0.6626909065  0.328074922
## [124,] -0.828623295  0.9103219462  0.1692381139 -0.039507101
## [125,]  1.363011889  1.9190638316 -0.9734089498  0.839966602
## [126,]  0.628437935 -1.4678997405 -0.0810134072  0.957937339
## [127,] -0.975627392  0.2922822335 -0.1847329454 -0.143685992
## [128,] -0.786447467  1.1148615610  0.2867993966  0.002900062
## [129,]  0.109524253 -0.2144488512  1.4868950745  0.620044181
## [130,] -1.004548410  0.0626851796 -0.3178767123 -0.213847271
## [131,] -1.050928035 -0.4498724749 -0.6162751199 -0.392745247
## [132,] -0.767938660 -1.2821877249 -1.1237885725 -1.122022726
## [133,] -0.954730098 -0.8758095964 -0.8728793137 -0.706410971
## [134,]  0.292191896  0.1041801184  1.6625351704  0.542869023
## [135,] -0.387165823  0.3076536277 -0.2134036318 -0.857242604
## [136,] -0.462102217  2.1341376573  0.8653228600  0.074412689
## [137,] -0.108437846 -0.9976529748 -1.7964107906 -0.249065381
## [138,] -0.196474743 -2.4582058055  0.1872334484 -0.036999327
## [139,] -1.034572211 -0.2229882265 -0.4839212327 -0.308444193
## [140,]  1.014114107  2.1229286683 -0.8311843925  1.360968857
## [141,] -1.054582031 -0.3948231038 -0.5836733895 -0.362956740
## [142,]  1.877062338  0.6748120111  0.3011724864  1.963921497
## [143,] -0.914197553  0.3055448384 -0.1808713113 -0.212813780
## [144,] -1.037266068  0.6140041188  0.0083808710  0.079736514
## [145,] -0.819925729 -0.8467055469 -0.8644051723 -0.858108061
## [146,] -0.776470582 -1.2840297533 -1.1243249106 -1.112421644
## [147,] -0.042176813 -2.2573783381  0.2954272933 -0.133602918
## [148,] -0.650385190  1.2000754541  0.3281840430 -0.124535951
## [149,] -0.047950783  1.0255835534 -0.6106769508  0.607226009
## [150,] -0.939278650  0.6351594471  0.0145406064 -0.030529989
## [151,]  0.024380066 -0.6795374501  1.2188912589  0.510445084
## [152,] -0.984345239 -0.3238208286 -0.5464266984 -0.416318488
## [153,] -0.122381475 -1.4371204529  0.7828568729  0.341801696
## [154,] -0.925047347 -1.2044307154 -1.0680019599 -0.893873062
## [155,]  1.826492899  0.3288645715  0.1010049859  1.866768227
## [156,]  3.390087901  1.4481779364  0.6589365139  0.466707308
## [157,] -0.894706997  0.9798119742  0.2143310710  0.073372667
## [158,] -0.026636433 -1.1372579352  0.9530327956  0.362441660
## [159,] -0.970386917  0.1817371177 -0.2500663755 -0.200936402
## [160,] -0.969406870  0.5169782861 -0.0530161888 -0.047979551
## [161,]  0.655880718  1.4592848861 -1.1984338560  1.494489006
## [162,] -1.052152140 -0.3942984941 -0.5835206404 -0.365691128
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## [620,]  2.555909698  0.4812366788  1.7391753012 -2.055874986
## [621,]  1.374501807 -1.4997057412 -0.9451826323  1.579424450
## [622,]  0.474767141 -1.4198735389  0.7547322762 -0.381530563
## [623,] -0.709603452  0.2938781176 -0.2008414417 -0.468722773
## [624,] -1.019922772  0.0035276162 -0.3516746131 -0.222222922
## [625,] -1.017440758  0.0040634791 -0.3515185874 -0.225015964
## [626,] -0.133206306 -1.4952957797  0.7493449671  0.328306399
## [627,] -0.082929597 -0.7687927323 -1.6634815589 -0.175063669
## [628,] -1.005126093 -1.3333961158 -1.1386987707 -0.855112655
## [629,]  1.552283925  1.6807360493 -1.1256679827  0.498593253
## [630,] -0.842145536 -0.4606349272 -0.6359819570 -0.653367498
## [631,] -1.009426336  0.0057937801 -0.3510147807 -0.234034697
## [632,] -0.856803991  0.8204803841  0.1182194599 -0.046309928
## [633,]  0.293242383  0.3277599687  1.7939269256  0.644393371
## [634,] -0.035567539 -0.7483183059  1.1822913721  0.552228276
## [635,]  0.557088374  0.5724626993 -1.7135313522  1.207673719
## [636,]  0.149998204 -0.7640932190  1.1611250713  0.317732140
## [637,] -0.888689303  0.5344050809 -0.0479420797 -0.138812068
## [638,]  0.182436410 -0.7012515988  1.1959956482  0.306905627
## [639,]  0.292515584 -0.4948547042 -0.7288114561 -2.058599349
## [640,]  0.384432832 -1.1165091774 -2.6955386055  0.642450851
## [641,] -1.008099402  0.1177567890 -0.2852685068 -0.184174676
## [642,] -0.972663098  0.3487604828 -0.1517151727 -0.121345131
## [643,] -1.018134881  0.7856493007  0.1080777947  0.135237798
## [644,] -0.129741415 -1.4945477152  0.7495627788  0.324407312
## [645,] -0.856803991  0.8204803841  0.1182194599 -0.046309928
## [646,]  0.528400872 -0.5148818937  1.2834067033 -0.031059397
## [647,] -1.003152277  0.0629866024 -0.3177889479 -0.215418357
## [648,] -0.718431729  0.8503547364  0.1269178881 -0.202022016
## [649,] -0.913337412  0.5849218563 -0.0166600920 -0.085398616
## [650,]  0.085370444 -2.1181645613  0.3691080939 -0.225780251
## [651,] -0.972438860  0.3208897639 -0.1681167914 -0.134435778
## [652,] -0.095994593 -1.2080705149  0.9158413376  0.414814671
## [653,]  0.932975224  0.7094543375 -1.6570707304  0.810360028
## [654,] -0.912581690  1.0317911193  0.2460388526  0.119163907
## [655,] -0.856828781 -0.7988345942 -0.8338935611 -0.790903964
## [656,]  1.150931821  0.6804485484  1.9463377286 -0.243745737
## [657,] -0.987157412  0.1222781315 -0.2839520407 -0.207740967
## [658,] -1.024511943  0.7284342401  0.0748454868  0.116737370
## [659,] -0.014020532 -0.9670193932  1.0523201521  0.425274679
## [660,] -0.761561598 -1.2249726642 -1.0905562646 -1.103522298
## [661,]  0.741663353 -1.0069974816 -2.6540399679  0.255347188
## [662,]  1.476918676 -1.3659175755 -0.8730815910  1.515526666
## [663,] -1.028858569 -1.3480124243 -1.1457719968 -0.832771220
## [664,] -1.022696720 -0.1087478006 -0.4175118499 -0.270454600
## [665,] -1.049049623 -0.3936286656 -0.5833256084 -0.369182430
## [666,]  2.482590756  0.1913237442 -0.0219082027  1.000069775
## [667,] -1.025419786 -0.2210122323 -0.4833458882 -0.318743535
## [668,] -0.361657574  0.5365138702 -0.0804744001 -0.783240892
## [669,] -1.040949274 -0.2802032871 -0.5171535406 -0.326944621
## [670,] -1.034501597 -0.5021642958 -0.6480739424 -0.436906748
## [671,]  1.777909122 -0.4633602706 -0.3616891289  1.561967520
## [672,]  0.575960104  0.8278092592 -1.5646035940  1.301981901
## [673,] -1.050928035 -0.4498724749 -0.6162751199 -0.392745247
## [674,] -0.905307677  0.9775233041  0.2136646856  0.085301749
## [675,]  0.597246238  0.8603240333 -1.5468497792  1.290866650
## [676,] -0.678750309  0.2447009992 -0.2317333654 -0.529118830
## [677,] -0.853207174 -1.1330822729 -1.0306544763 -0.949039115
## [678,] -0.698449416  2.8090080902  1.2772740678  0.674173273
## [679,]  1.448480112 -1.7070869943 -1.0718578891  1.393469238
## [680,]  0.249972874 -1.5242445278  0.7077697138 -0.154243300
## [681,]  0.262235704  0.0418743610  1.6278206191  0.550902494
## [682,] -0.110195557 -1.4903277955  0.7507914806  0.302412107
## [683,]  1.991958015  0.4711569300  1.7693867405 -1.369899663
## [684,] -0.612122816  1.5433658179  0.5275778906 -0.013533383
## [685,]  1.593931448 -0.8381103369 -0.5702430064  1.614940254
## [686,] -0.830295788  0.9378799892  0.1855486917 -0.024786714
## [687,] -0.990206217 -0.2134096785 -0.4811322747 -0.358369817
## [688,]  0.286865320  0.2705449081  1.7606946177  0.625892943
## [689,] -0.952459927 -0.0377455255 -0.3802651588 -0.323816348
## [690,]  0.088150689 -0.1073868437  1.5512143381  0.695449364
## [691,]  1.546048265 -0.6809334511 -0.4747587744  1.745853671
## [692,] -0.442495047  0.4632229249 -0.1183874766 -0.717950062
## [693,] -1.103167049 -1.1870482139 -1.0463675823 -0.667756051
## [694,] -1.003049274  0.0630088408 -0.3177824728 -0.215534269
## [695,]  0.610906330  0.2846665856  1.7482332202  0.235568806
## [696,] -0.994346913  0.4557555074 -0.0874154123 -0.045590818
## [697,] -0.855427766  1.2674836128  0.3809574109  0.157554335
## [698,]  1.678284518 -0.5965455906 -0.4336146414  1.622723132
## [699,]  1.387203810 -1.3852868731 -0.8787212930  1.616483960
## [700,] -1.017112014 -0.2750568606 -0.5156550705 -0.353768996
## [701,] -1.047688710 -0.3374965837 -0.5504086282 -0.345037265
## [702,]  2.591000816  1.1639797750  0.5430410319  1.314577051
## [703,]  0.141071518 -1.0452117911  0.9964067687  0.199394362
## [704,] -0.958409837  0.4635142652 -0.0851563174 -0.086031273
## [705,] -0.070208481 -1.2583415972  0.8846308877  0.360120609
## [706,] -0.957976849  0.1844164318 -0.2492862474 -0.214901612
## [707,] -1.019922772  0.0035276162 -0.3516746131 -0.222222922
## [708,]  1.040582830 -0.0946382622  0.7000179410  1.084707607
## [709,] -0.933328740  0.1338996565 -0.2805682351 -0.268315064
## [710,]  0.152449418 -1.3777848985  0.8001334335  0.032530955
## [711,]  0.814167311  0.4046125825 -1.8286964431  0.815673010
## [712,] -0.195145312  0.5470983840 -0.8825814068  0.567452960
attach(Temp2)
## The following objects are masked from train:
## 
##     Age, Embarked, Fare, Sex, Survived
library(dplyr)
## Warning: package 'dplyr' was built under R version 4.2.2
## 
## Attaching package: 'dplyr'
## 
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## 
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
# Identifying the scores by their survival status
titanictyp_pca <- cbind(data.frame(Survived),Temp2_pca$x)
titanictyp_pca
##     Survived          PC1           PC2           PC3          PC4
## 1          0 -1.036571945 -0.1675817029 -0.4512155112 -0.280517248
## 2          1  2.328844131  0.1022918285 -0.0644045317  1.147406212
## 3          1 -0.076863406 -1.0364253330  1.0155382614  0.470315955
## 4          1  0.541154997 -0.4004517724  1.3498713191  0.005941459
## 5          0 -0.943742080  0.5783575367 -0.0185714058 -0.051183852
## 6          0 -0.278861772  1.7828311382  0.6470218066 -0.311526470
## 7          0 -0.992543997 -1.2748413981 -1.1050763987 -0.843594832
## 8          1 -0.030671121 -0.9706142289  1.0512734542  0.444011801
## 9          1  1.664344689 -1.3812908595 -0.8941309506  1.278937145
## 10         1 -0.108260428 -2.2716456857  0.2912731112 -0.059238176
## 11         1  0.358340114  0.8443588327  2.0935020004  0.802227620
## 12         0 -1.039398015 -0.2798683728 -0.5170560246 -0.328690272
## 13         0 -0.630009991  0.8694448494  0.1324763008 -0.301524135
## 14         0 -0.154266787 -1.7231957561  0.6166953333  0.249299556
## 15         1  0.208282705  0.6444468869  1.9855747253  0.894059299
## 16         0 -0.121191971 -1.1120830961 -1.8628754064 -0.286066237
## 17         0  0.080053345 -0.7233559402  1.1895595915  0.422118607
## 18         0 -0.720981351  0.6264512250 -0.0045681066 -0.301859366
## 19         1 -0.888689303  0.5344050809 -0.0479420797 -0.138812068
## 20         1  0.625733012 -1.5243219921 -0.1140148752  0.935304605
## 21         1 -0.647725138  0.2513992845 -0.2297830451 -0.564031854
## 22         0 -0.028458129 -2.0310634439  0.4276154032 -0.046334256
## 23         1  0.290832573 -0.2869811981  1.4326297117  0.364662359
## 24         0  2.118171868  0.3460076983 -0.3513946758 -3.907620912
## 25         0  0.875161156  1.1995167387 -1.3652222002  1.106508508
## 26         0 -0.715648479  2.3585887361  1.0135414535  0.488114652
## 27         0  1.474364633  0.6588246642 -1.7215319207  0.124097704
## 28         0 -0.353680136  1.0966188162  0.2483413792 -0.535451822
## 29         0 -1.033020953 -0.2226533122 -0.4838237166 -0.310189844
## 30         0 -0.002848466 -1.4671517284  0.7575395885  0.181613043
## 31         1  1.430674269 -1.4317399327 -0.9088200604  1.541889474
## 32         0  0.031651073 -0.2312615472  1.4819997708  0.707675872
## 33         0  0.091775301 -0.9441782404  1.0589707441  0.306221266
## 34         1  1.737017034 -1.9798219080 -1.2507083116  0.914715217
## 35         1  0.649379751 -1.2958636466  0.0187973373  1.011401099
## 36         0 -0.005330479 -1.4676875913  0.7573835629  0.184406085
## 37         0 -0.729676286 -0.9388973610 -0.9243947250 -1.011020158
## 38         0 -1.036123470 -0.2233231407 -0.4840187487 -0.306698542
## 39         1  2.466575808  0.7462487722  0.3053993550  1.274857785
## 40         1  0.166579768 -0.8163515486  1.1293360004  0.273396074
## 41         0  1.459736803  2.7216822690 -0.5076885621  1.090593468
## 42         1 -0.076792792 -1.3156014023  0.8513855516  0.341853400
## 43         0  0.547522780  0.4866401084 -1.7633798140  1.179923077
## 44         1  0.035247891 -2.1848242042  0.3331258345 -0.195053315
## 45         0 -0.614660418 -0.6907125655 -0.7858388195 -1.037742521
## 46         0  0.506071875  0.1147422142 -1.9793898155  1.059670295
## 47         0  0.056057955  1.3525954097  0.3725928346 -0.919505513
## 48         0 -0.895091155 -1.1421249580 -1.0332874086 -0.901906532
## 49         1 -0.025776293 -0.8578809172  1.1172440150  0.489856824
## 50         0 -1.044431067 -0.3367932638 -0.5502038446 -0.348703132
## 51         1 -0.134256967 -1.5513608787  0.7164474901  0.303812103
## 52         0 -0.993534474  0.0650630709 -0.3171843486 -0.226241395
## 53         0 -0.932468599  0.4132766744 -0.1163570157 -0.140899900
## 54         0  0.343048387 -1.5041496720  0.7136206745 -0.258982373
## 55         0 -0.220781974 -0.0472922039 -0.4327643331 -1.224212819
## 56         0  0.621242869  0.3629605012 -1.8408241584  1.032773366
## 57         1 -0.361657574  0.5365138702 -0.0804744001 -0.783240892
## 58         0 -1.012476731  0.0051352047 -0.3512065362 -0.230602048
## 59         1 -0.901655367 -1.3205494547 -1.1377756838 -0.975914620
## 60         1  0.005110655 -0.7953742112  1.1520170759  0.480775963
## 61         0 -1.014854325 -0.1628929032 -0.4498502870 -0.304956365
## 62         1 -0.964009855  0.2389521784 -0.2168340676 -0.182435974
## 63         0 -0.503768344  0.2824793282 -0.2207335593 -0.726028287
## 64         1 -0.102301041 -1.5444616449  0.7184563199  0.267851688
## 65         1  0.066125823 -0.6146863442  1.2543469319  0.489144664
## 66         0 -0.738211213 -0.4381956715 -0.6294483843 -0.770326129
## 67         1  3.069503611 -0.5246444689  1.1148325103 -3.147361192
## 68         0 -1.013889766 -0.0510081303 -0.3841267929 -0.254688560
## 69         0 -0.982004454  0.2350671729 -0.2179652533 -0.162186420
## 70         0 -1.041827907 -0.2803929825 -0.5172087736 -0.325955884
## 71         0 -0.214309508  1.3500617657  0.3884282861 -0.589580909
## 72         0 -0.845699534  0.0969804002 -0.3078910727 -0.392601955
## 73         0 -0.800620638  1.9493755407  0.7783798817  0.403998588
## 74         0  1.158894058  2.9917603749 -0.3296117147  1.583195391
## 75         1  1.209014909  0.3223447643 -1.9023696200  0.294316071
## 76         1  0.161234875 -0.5383141877  1.2931571557  0.407793843
## 77         0 -0.727358414  0.5692361643 -0.0378004145 -0.320359794
## 78         0 -0.064471655 -0.9220734477  1.0819800975  0.507724595
## 79         0 -0.173778840 -0.0371443017 -0.4298095980 -1.277106050
## 80         0 -0.948998041  0.4655462570 -0.0845646682 -0.096622488
## 81         0 -0.932539213  0.6924527437  0.0477956940 -0.012437345
## 82         0 -0.990295149  0.1774389620 -0.2513178570 -0.178533413
## 83         1 -0.112161487 -1.3232374475  0.8491621866  0.381654248
## 84         0 -0.926524525  0.7495895684  0.0810052222  0.006470867
## 85         0 -0.321794824  1.3826941194  0.4145029188 -0.442949682
## 86         0  1.473730145 -1.3945251058 -0.8896977450  1.506276452
## 87         0 -1.026643890 -0.1654382516 -0.4505914087 -0.291689416
## 88         0 -0.091546650 -1.3746250000  0.8176266572  0.332779489
## 89         0  1.489723682 -1.2514764691 -0.8066137767  1.552470265
## 90         0 -1.034572211 -0.2229882265 -0.4839212327 -0.308444193
## 91         0  0.050371589  2.7498782185  0.3968624480  1.279719438
## 92         0 -0.821294068  0.2697642906 -0.2078625945 -0.343035886
## 93         0  3.500861199  0.8729890093 -1.7254669726 -2.259051431
## 94         0  0.059862195 -2.3470248039  0.2361788623 -0.299781963
## 95         0 -0.220781974 -0.0472922039 -0.4327643331 -1.224212819
## 96         0  0.856496849  0.7767001720 -1.6126312086  0.934937055
## 97         1  0.027568597 -0.6509299197  1.2355074129  0.519695298
## 98         0  0.036664218  1.8509526994  0.6668565633 -0.666591926
## 99         1  0.492096651 -0.4466576443 -2.3085826307  0.818630611
## 100        1 -1.025161831 -0.0534417513 -0.3848353832 -0.242003960
## 101        0 -0.893312280  1.1476278804  0.3129130357  0.148833028
## 102        0  0.584492113  0.7458939120 -1.6133143950  1.253865794
## 103        0 -1.051808084 -0.2825476869 -0.5178361527 -0.314725062
## 104        0  0.138651104  0.1827074307  1.7185460698  0.767003689
## 105        1  0.166579768 -0.8163515486  1.1293360004  0.273396074
## 106        0 -0.946082865  0.0194695352 -0.3470328509 -0.305315920
## 107        0  0.609453478  0.1929004015 -1.9400595584  0.969010264
## 108        1  0.106324917 -1.3877431053  0.7972339315  0.084435450
## 109        0 -0.371914372  0.8134907585  0.0830379805 -0.643315693
## 110        0 -1.050427438 -0.5056026596 -0.6490750808 -0.418985194
## 111        0  1.411988553  0.4220047153 -1.8567787569  0.091583837
## 112        1 -0.104543417 -1.2657544555  0.8824725073  0.398758155
## 113        1  0.008732262 -1.1296218900  0.9552561607  0.322640812
## 114        0 -0.290457192 -0.1993767184 -1.3153815378  0.340912606
## 115        0 -1.009337404 -0.3850548604 -0.5808291985 -0.413871101
## 116        0 -0.689606114 -0.2601871186 -0.5278986563 -0.747992218
## 117        1 -0.997913218  0.1199559700 -0.2846281777 -0.195637320
## 118        0  0.142972844 -1.9382135057  0.4712234148 -0.213571117
## 119        0 -0.711415758  0.7122738159  0.0452803553 -0.274108724
## 120        0 -0.837672804  0.9921255660  0.2179163837  0.009191356
## 121        0 -0.786174026  1.5057884376  0.5166365941  0.182328683
## 122        1  0.625789110 -1.1080768203  0.9283830454 -0.423094436
## 123        0 -0.813012301  1.7512662798  0.6626909065  0.328074922
## 124        0 -0.828623295  0.9103219462  0.1692381139 -0.039507101
## 125        0  1.363011889  1.9190638316 -0.9734089498  0.839966602
## 126        1  0.628437935 -1.4678997405 -0.0810134072  0.957937339
## 127        0 -0.975627392  0.2922822335 -0.1847329454 -0.143685992
## 128        0 -0.786447467  1.1148615610  0.2867993966  0.002900062
## 129        1  0.109524253 -0.2144488512  1.4868950745  0.620044181
## 130        0 -1.004548410  0.0626851796 -0.3178767123 -0.213847271
## 131        0 -1.050928035 -0.4498724749 -0.6162751199 -0.392745247
## 132        0 -0.767938660 -1.2821877249 -1.1237885725 -1.122022726
## 133        1 -0.954730098 -0.8758095964 -0.8728793137 -0.706410971
## 134        0  0.292191896  0.1041801184  1.6625351704  0.542869023
## 135        0 -0.387165823  0.3076536277 -0.2134036318 -0.857242604
## 136        0 -0.462102217  2.1341376573  0.8653228600  0.074412689
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## 607        0 -0.916959019  0.9191695350  0.1801008232  0.072736535
## 608        1  0.493317750  0.0003120929 -2.0458544313  1.022669439
## 609        1  1.377765637 -0.1639905980  1.4352941963 -0.909830642
## 610        0 -1.068319034 -0.5094654268 -0.6501997915 -0.398851551
## 611        1  0.951681199  0.5815923917  1.9009809039 -0.045203065
## 612        0  0.721112588 -0.6382366167  0.4008680858  1.225960326
## 613        0 -0.958995120  0.4075496405 -0.1180245395 -0.111049264
## 614        0 -0.995895167 -0.0471231248 -0.3829956072 -0.274938114
## 615        0 -0.863270160  1.3216287153  0.4132958480  0.192056100
## 616        0  0.152781454  0.7441407806  2.0477486367  1.007868808
## 617        1  0.288776122  0.6059870250  1.9578033140  0.777802403
## 618        0 -1.055875161 -0.3951022883 -0.5837546788 -0.361501565
## 619        1 -0.154315904 -2.2257507272  0.3212093779  0.018265263
## 620        1  2.555909698  0.4812366788  1.7391753012 -2.055874986
## 621        1  1.374501807 -1.4997057412 -0.9451826323  1.579424450
## 622        1  0.474767141 -1.4198735389  0.7547322762 -0.381530563
## 623        0 -0.709603452  0.2938781176 -0.2008414417 -0.468722773
## 624        0 -1.019922772  0.0035276162 -0.3516746131 -0.222222922
## 625        0 -1.017440758  0.0040634791 -0.3515185874 -0.225015964
## 626        1 -0.133206306 -1.4952957797  0.7493449671  0.328306399
## 627        0 -0.082929597 -0.7687927323 -1.6634815589 -0.175063669
## 628        1 -1.005126093 -1.3333961158 -1.1386987707 -0.855112655
## 629        0  1.552283925  1.6807360493 -1.1256679827  0.498593253
## 630        0 -0.842145536 -0.4606349272 -0.6359819570 -0.653367498
## 631        0 -1.009426336  0.0057937801 -0.3510147807 -0.234034697
## 632        0 -0.856803991  0.8204803841  0.1182194599 -0.046309928
## 633        1  0.293242383  0.3277599687  1.7939269256  0.644393371
## 634        1 -0.035567539 -0.7483183059  1.1822913721  0.552228276
## 635        0  0.557088374  0.5724626993 -1.7135313522  1.207673719
## 636        0  0.149998204 -0.7640932190  1.1611250713  0.317732140
## 637        0 -0.888689303  0.5344050809 -0.0479420797 -0.138812068
## 638        1  0.182436410 -0.7012515988  1.1959956482  0.306905627
## 639        1  0.292515584 -0.4948547042 -0.7288114561 -2.058599349
## 640        1  0.384432832 -1.1165091774 -2.6955386055  0.642450851
## 641        1 -1.008099402  0.1177567890 -0.2852685068 -0.184174676
## 642        0 -0.972663098  0.3487604828 -0.1517151727 -0.121345131
## 643        0 -1.018134881  0.7856493007  0.1080777947  0.135237798
## 644        0 -0.129741415 -1.4945477152  0.7495627788  0.324407312
## 645        0 -0.856803991  0.8204803841  0.1182194599 -0.046309928
## 646        1  0.528400872 -0.5148818937  1.2834067033 -0.031059397
## 647        0 -1.003152277  0.0629866024 -0.3177889479 -0.215418357
## 648        0 -0.718431729  0.8503547364  0.1269178881 -0.202022016
## 649        0 -0.913337412  0.5849218563 -0.0166600920 -0.085398616
## 650        0  0.085370444 -2.1181645613  0.3691080939 -0.225780251
## 651        0 -0.972438860  0.3208897639 -0.1681167914 -0.134435778
## 652        0 -0.095994593 -1.2080705149  0.9158413376  0.414814671
## 653        0  0.932975224  0.7094543375 -1.6570707304  0.810360028
## 654        0 -0.912581690  1.0317911193  0.2460388526  0.119163907
## 655        0 -0.856828781 -0.7988345942 -0.8338935611 -0.790903964
## 656        1  1.150931821  0.6804485484  1.9463377286 -0.243745737
## 657        1 -0.987157412  0.1222781315 -0.2839520407 -0.207740967
## 658        0 -1.024511943  0.7284342401  0.0748454868  0.116737370
## 659        1 -0.014020532 -0.9670193932  1.0523201521  0.425274679
## 660        0 -0.761561598 -1.2249726642 -1.0905562646 -1.103522298
## 661        1  0.741663353 -1.0069974816 -2.6540399679  0.255347188
## 662        1  1.476918676 -1.3659175755 -0.8730815910  1.515526666
## 663        1 -1.028858569 -1.3480124243 -1.1457719968 -0.832771220
## 664        0 -1.022696720 -0.1087478006 -0.4175118499 -0.270454600
## 665        0 -1.049049623 -0.3936286656 -0.5833256084 -0.369182430
## 666        1  2.482590756  0.1913237442 -0.0219082027  1.000069775
## 667        0 -1.025419786 -0.2210122323 -0.4833458882 -0.318743535
## 668        1 -0.361657574  0.5365138702 -0.0804744001 -0.783240892
## 669        0 -1.040949274 -0.2802032871 -0.5171535406 -0.326944621
## 670        0 -1.034501597 -0.5021642958 -0.6480739424 -0.436906748
## 671        1  1.777909122 -0.4633602706 -0.3616891289  1.561967520
## 672        0  0.575960104  0.8278092592 -1.5646035940  1.301981901
## 673        0 -1.050928035 -0.4498724749 -0.6162751199 -0.392745247
## 674        0 -0.905307677  0.9775233041  0.2136646856  0.085301749
## 675        0  0.597246238  0.8603240333 -1.5468497792  1.290866650
## 676        0 -0.678750309  0.2447009992 -0.2317333654 -0.529118830
## 677        0 -0.853207174 -1.1330822729 -1.0306544763 -0.949039115
## 678        0 -0.698449416  2.8090080902  1.2772740678  0.674173273
## 679        0  1.448480112 -1.7070869943 -1.0718578891  1.393469238
## 680        1  0.249972874 -1.5242445278  0.7077697138 -0.154243300
## 681        0  0.262235704  0.0418743610  1.6278206191  0.550902494
## 682        1 -0.110195557 -1.4903277955  0.7507914806  0.302412107
## 683        1  1.991958015  0.4711569300  1.7693867405 -1.369899663
## 684        1 -0.612122816  1.5433658179  0.5275778906 -0.013533383
## 685        1  1.593931448 -0.8381103369 -0.5702430064  1.614940254
## 686        0 -0.830295788  0.9378799892  0.1855486917 -0.024786714
## 687        0 -0.990206217 -0.2134096785 -0.4811322747 -0.358369817
## 688        1  0.286865320  0.2705449081  1.7606946177  0.625892943
## 689        0 -0.952459927 -0.0377455255 -0.3802651588 -0.323816348
## 690        1  0.088150689 -0.1073868437  1.5512143381  0.695449364
## 691        1  1.546048265 -0.6809334511 -0.4747587744  1.745853671
## 692        0 -0.442495047  0.4632229249 -0.1183874766 -0.717950062
## 693        1 -1.103167049 -1.1870482139 -1.0463675823 -0.667756051
## 694        0 -1.003049274  0.0630088408 -0.3177824728 -0.215534269
## 695        1  0.610906330  0.2846665856  1.7482332202  0.235568806
## 696        0 -0.994346913  0.4557555074 -0.0874154123 -0.045590818
## 697        0 -0.855427766  1.2674836128  0.3809574109  0.157554335
## 698        1  1.678284518 -0.5965455906 -0.4336146414  1.622723132
## 699        1  1.387203810 -1.3852868731 -0.8787212930  1.616483960
## 700        0 -1.017112014 -0.2750568606 -0.5156550705 -0.353768996
## 701        0 -1.047688710 -0.3374965837 -0.5504086282 -0.345037265
## 702        1  2.591000816  1.1639797750  0.5430410319  1.314577051
## 703        1  0.141071518 -1.0452117911  0.9964067687  0.199394362
## 704        0 -0.958409837  0.4635142652 -0.0851563174 -0.086031273
## 705        0 -0.070208481 -1.2583415972  0.8846308877  0.360120609
## 706        0 -0.957976849  0.1844164318 -0.2492862474 -0.214901612
## 707        0 -1.019922772  0.0035276162 -0.3516746131 -0.222222922
## 708        0  1.040582830 -0.0946382622  0.7000179410  1.084707607
## 709        0 -0.933328740  0.1338996565 -0.2805682351 -0.268315064
## 710        1  0.152449418 -1.3777848985  0.8001334335  0.032530955
## 711        1  0.814167311  0.4046125825 -1.8286964431  0.815673010
## 712        0 -0.195145312  0.5470983840 -0.8825814068  0.567452960
# Means of scores for all the PC's classified by Survival status
length(titanictyp_pca[, 2:5])
## [1] 4
length(Temp2$Survived)
## [1] 712
Temp2$Survived <- factor(Temp2$Survived, levels = c(0, 1))
tabmeansPC <- aggregate(titanictyp_pca[,2:5],by=list(Survived=Temp2$Survived),mean)
tabmeansPC
##   Survived        PC1        PC2        PC3         PC4
## 1        0 -0.4248113  0.2427335 -0.1708880 -0.04404456
## 2        1  0.6254167 -0.3573577  0.2515851  0.06484338
tabmeansPC <- tabmeansPC[rev(order(tabmeansPC$Survived)),]
tabmeansPC
##   Survived        PC1        PC2        PC3         PC4
## 2        1  0.6254167 -0.3573577  0.2515851  0.06484338
## 1        0 -0.4248113  0.2427335 -0.1708880 -0.04404456
tabfmeans <- t(tabmeansPC[,-1])
tabfmeans
##               2           1
## PC1  0.62541668 -0.42481133
## PC2 -0.35735772  0.24273355
## PC3  0.25158512 -0.17088801
## PC4  0.06484338 -0.04404456
colnames(tabfmeans) <- t(as.vector(tabmeansPC[1]$Survived))
tabfmeans
##               1           0
## PC1  0.62541668 -0.42481133
## PC2 -0.35735772  0.24273355
## PC3  0.25158512 -0.17088801
## PC4  0.06484338 -0.04404456
# Standard deviations of scores for all the PC's classified by Survival status
tabsdsPC <- aggregate(titanictyp_pca[,2:5],by=list(Survived=Temp2$Survived),sd)
tabfsds <- t(tabsdsPC[,-1])
colnames(tabfsds) <- t(as.vector(tabsdsPC[1]$Survived))
tabfsds
##             0        1
## PC1 0.7837685 1.376398
## PC2 0.9805745 1.025566
## PC3 0.7769647 1.036368
## PC4 0.6478594 1.034475
t.test(PC1~Temp2$Survived,data=titanictyp_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC1 by Temp2$Survived
## t = -11.722, df = 413.73, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
##  -1.2263414 -0.8741146
## sample estimates:
## mean in group 0 mean in group 1 
##      -0.4248113       0.6254167
t.test(PC2~Temp2$Survived,data=titanictyp_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC2 by Temp2$Survived
## t = 7.7995, df = 597.72, p-value = 2.782e-14
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
##  0.4489854 0.7511971
## sample estimates:
## mean in group 0 mean in group 1 
##       0.2427335      -0.3573577
t.test(PC3~Temp2$Survived,data=titanictyp_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC3 by Temp2$Survived
## t = -5.8852, df = 498.65, p-value = 7.302e-09
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
##  -0.5635121 -0.2814342
## sample estimates:
## mean in group 0 mean in group 1 
##      -0.1708880       0.2515851
t.test(PC4~Temp2$Survived,data=titanictyp_pca)
## 
##  Welch Two Sample t-test
## 
## data:  PC4 by Temp2$Survived
## t = -1.5873, df = 439.14, p-value = 0.1132
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
##  -0.24370885  0.02593297
## sample estimates:
## mean in group 0 mean in group 1 
##     -0.04404456      0.06484338
## F ratio tests
var.test(PC1~Temp2$Survived,data=titanictyp_pca)
## 
##  F test to compare two variances
## 
## data:  PC1 by Temp2$Survived
## F = 0.32426, num df = 423, denom df = 287, p-value < 2.2e-16
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.2616503 0.4000869
## sample estimates:
## ratio of variances 
##          0.3242558
var.test(PC2~Temp2$Survived,data=titanictyp_pca)
## 
##  F test to compare two variances
## 
## data:  PC2 by Temp2$Survived
## F = 0.91419, num df = 423, denom df = 287, p-value = 0.4019
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.7376795 1.1279785
## sample estimates:
## ratio of variances 
##          0.9141855
var.test(PC3~Temp2$Survived,data=titanictyp_pca)
## 
##  F test to compare two variances
## 
## data:  PC3 by Temp2$Survived
## F = 0.56205, num df = 423, denom df = 287, p-value = 6.934e-08
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.4535319 0.6934912
## sample estimates:
## ratio of variances 
##          0.5620493
var.test(PC4~Temp2$Survived,data=titanictyp_pca)
## 
##  F test to compare two variances
## 
## data:  PC4 by Temp2$Survived
## F = 0.39221, num df = 423, denom df = 287, p-value < 2.2e-16
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.3164865 0.4839364
## sample estimates:
## ratio of variances 
##          0.3922128
# Levene's tests (one-sided)
library(car)
## Warning: package 'car' was built under R version 4.2.2
## Loading required package: carData
## Warning: package 'carData' was built under R version 4.2.2
## 
## Attaching package: 'car'
## 
## The following object is masked from 'package:dplyr':
## 
##     recode
(LTPC1 <- leveneTest(PC1~Temp2$Survived,data=titanictyp_pca))
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   1  42.423 1.392e-10 ***
##       710                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(p_PC1_1sided <- LTPC1[[3]][1]/2)
## [1] 6.959925e-11
(LTPC2 <- leveneTest(PC2~Temp2$Survived,data=titanictyp_pca))
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)  
## group   1  3.0413 0.0816 .
##       710                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(p_PC2_1sided=LTPC2[[3]][1]/2)
## [1] 0.04080225
(LTPC3 <- leveneTest(PC3~Temp2$Survived,data=titanictyp_pca))
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   1  46.202 2.262e-11 ***
##       710                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(p_PC3_1sided <- LTPC3[[3]][1]/2)
## [1] 1.131124e-11
(LTPC4 <- leveneTest(PC4~Temp2$Survived,data=titanictyp_pca))
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   1  31.576 2.756e-08 ***
##       710                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(p_PC4_1sided <- LTPC4[[3]][1]/2)
## [1] 1.378021e-08
# Plotting the scores for the first and second components
plot(titanictyp_pca$PC1, titanictyp_pca$PC2,pch=ifelse(titanictyp_pca$Survived == "S",1,16),xlab="PC1", ylab="PC2", main="49 Temp2 against values for PC1 & PC2")
abline(h=0)
abline(v=0)
legend("bottomleft", legend=c("Survivor","Nonsurvivor"), pch=c(1,16))

plot(eigen_Temp2, xlab = "Component number", ylab = "Component variance", type = "l", main = "Scree diagram")

plot(log(eigen_Temp2), xlab = "Component number",ylab = "log(Component variance)", type="l",main = "Log(eigenvalue) diagram")

print(summary(Temp2_pca))
## Importance of components:
##                           PC1    PC2    PC3    PC4
## Standard deviation     1.1816 1.0409 0.9142 0.8274
## Proportion of Variance 0.3491 0.2709 0.2089 0.1711
## Cumulative Proportion  0.3491 0.6199 0.8289 1.0000
diag(cov(Temp2_pca$x))
##       PC1       PC2       PC3       PC4 
## 1.3962390 1.0834721 0.8357525 0.6845364
xlim <- range(Temp2_pca$x[,1])
Temp2_pca$x[,1]
##   [1] -1.036571945  2.328844131 -0.076863406  0.541154997 -0.943742080
##   [6] -0.278861772 -0.992543997 -0.030671121  1.664344689 -0.108260428
##  [11]  0.358340114 -1.039398015 -0.630009991 -0.154266787  0.208282705
##  [16] -0.121191971  0.080053345 -0.720981351 -0.888689303  0.625733012
##  [21] -0.647725138 -0.028458129  0.290832573  2.118171868  0.875161156
##  [26] -0.715648479  1.474364633 -0.353680136 -1.033020953 -0.002848466
##  [31]  1.430674269  0.031651073  0.091775301  1.737017034  0.649379751
##  [36] -0.005330479 -0.729676286 -1.036123470  2.466575808  0.166579768
##  [41]  1.459736803 -0.076792792  0.547522780  0.035247891 -0.614660418
##  [46]  0.506071875  0.056057955 -0.895091155 -0.025776293 -1.044431067
##  [51] -0.134256967 -0.993534474 -0.932468599  0.343048387 -0.220781974
##  [56]  0.621242869 -0.361657574 -1.012476731 -0.901655367  0.005110655
##  [61] -1.014854325 -0.964009855 -0.503768344 -0.102301041  0.066125823
##  [66] -0.738211213  3.069503611 -1.013889766 -0.982004454 -1.041827907
##  [71] -0.214309508 -0.845699534 -0.800620638  1.158894058  1.209014909
##  [76]  0.161234875 -0.727358414 -0.064471655 -0.173778840 -0.948998041
##  [81] -0.932539213 -0.990295149 -0.112161487 -0.926524525 -0.321794824
##  [86]  1.473730145 -1.026643890 -0.091546650  1.489723682 -1.034572211
##  [91]  0.050371589 -0.821294068  3.500861199  0.059862195 -0.220781974
##  [96]  0.856496849  0.027568597  0.036664218  0.492096651 -1.025161831
## [101] -0.893312280  0.584492113 -1.051808084  0.138651104  0.166579768
## [106] -0.946082865  0.609453478  0.106324917 -0.371914372 -1.050427438
## [111]  1.411988553 -0.104543417  0.008732262 -0.290457192 -1.009337404
## [116] -0.689606114 -0.997913218  0.142972844 -0.711415758 -0.837672804
## [121] -0.786174026  0.625789110 -0.813012301 -0.828623295  1.363011889
## [126]  0.628437935 -0.975627392 -0.786447467  0.109524253 -1.004548410
## [131] -1.050928035 -0.767938660 -0.954730098  0.292191896 -0.387165823
## [136] -0.462102217 -0.108437846 -0.196474743 -1.034572211  1.014114107
## [141] -1.054582031  1.877062338 -0.914197553 -1.037266068 -0.819925729
## [146] -0.776470582 -0.042176813 -0.650385190 -0.047950783 -0.939278650
## [151]  0.024380066 -0.984345239 -0.122381475 -0.925047347  1.826492899
## [156]  3.390087901 -0.894706997 -0.026636433 -0.970386917 -0.969406870
## [161]  0.655880718 -1.052152140 -0.198422354 -0.866074733  0.675019418
## [166]  0.628645183  0.915856252 -1.026299834  0.142791800 -1.036571945
## [171] -0.914197553  2.805324565 -0.070486344 -0.663931846  2.352736343
## [176] -0.945222724 -1.064906265 -0.933328740 -0.841709082  0.092394215
## [181] -1.010510802 -1.015370410 -1.046137539 -0.990722301  0.918110825
## [186] -0.985417223 -0.723057710  0.080389515 -0.983485098 -0.663587790
## [191]  0.035763975 -1.015370410 -0.904063665 -0.951599786 -1.038123204
## [196]  0.557036252  0.902107564 -0.085101979 -0.008021331 -0.378687788
## [201] -0.599817166 -0.026241670 -0.541975130 -0.875726341  0.171281245
## [206]  1.576021360  0.923765970  7.783122743  0.300498078 -0.858188104
## [211]  0.053228880 -1.011757819 -0.906960350 -0.672282725 -1.010925472
## [216]  1.933332924  1.565398897 -1.107413754  0.162439072  0.880591976
## [221]  1.028205947  0.042129017 -0.089306659  0.133484249  0.015297746
## [226] -0.990811408 -1.046911665 -1.045775078  0.594006912 -0.957632792
## [231] -1.028557523 -0.837672804  0.666907557  0.803320697  2.453348419
## [236]  0.665415513 -0.078138217 -1.015803398  0.515637469  1.552483175
## [241]  4.592488314 -1.145676128  0.619772454  2.661751642  0.765215150
## [246]  2.099692269  2.386934820  4.572763956  0.147448581 -0.990295149
## [251] -0.666862335 -0.077742039  0.134694456 -0.748737987  1.902679142
## [256]  3.126121828 -1.036571945 -0.996672211  0.775010371  0.159170537
## [261]  3.114677909 -0.800431707  0.049888315  0.111388768  2.023443967
## [266] -0.622997025  0.879968183 -0.941426084 -0.255394947  3.132498891
## [271] -0.879971456 -0.539315078 -0.931424410  3.075880674 -0.926951678
## [276] -0.946082865 -0.875935179 -0.026636433  0.075396564 -1.050389038
## [281] -0.891501476 -1.005684998  0.461432438 -0.886514536 -0.970386917
## [286]  0.481832316  0.062642440 -0.665516910  0.805013470  1.668230548
## [291] -0.956152148 -0.985555446  2.518366521  2.214952369  1.123523486
## [296] -1.071439868 -1.045775078  2.099575543 -0.060343441 -0.110748452
## [301]  3.072971793  0.453398283 -1.049187846  4.293322569  1.403617766
## [306] -0.964424525  0.527503921 -0.239913161 -0.678431042  0.049888315
## [311]  1.459216011  0.451942143 -1.036175592 -0.989932775  2.754308066
## [316]  0.019280820 -1.029798530 -0.045856727 -0.650833665 -0.989862160
## [321] -0.005471708 -0.919785089 -1.001135641 -0.085169588 -0.891582983
## [326] -0.105973355 -0.789408756 -0.845432102 -1.015020343 -1.036433722
## [331]  1.757783372 -0.887899777  0.279130525 -0.064898808 -0.914197553
## [336]  0.022456956 -0.265500247 -0.984176216  0.016245912 -0.901214683
## [341]  0.160202706  0.102809144 -0.962873267 -0.758795250  0.249481579
## [346] -1.070008516 -0.254264370  1.237470265  0.219497592  0.044721460
## [351]  2.405139675 -0.938845662  0.271715283 -1.021403416 -1.010925472
## [356] -0.001128184 -0.225464960 -0.016118675 -0.720532876  1.472767262
## [361] -0.556725983 -0.692886669  0.811752906  1.694326912  0.558983863
## [366] -0.522843943  0.108142017 -0.631254003 -0.950119142 -0.489330748
## [371] -0.799410430 -0.937020961 -0.580237504  1.445664747 -0.917009726
## [376]  0.213805637  1.519713505 -0.078637400 -0.789408756 -0.994466645
## [381] -1.033211299 -0.175773979 -0.627414543 -0.848086144  0.179719640
## [386]  1.565787300  0.999086522  1.014510286 -0.975627392 -1.012126664
## [391] -1.042949008 -0.537594796  1.343183574 -1.033020953  2.517541600
## [396]  1.699155610 -1.017044405 -1.050928035  0.660530495  0.013916019
## [401]  0.834487097  1.742305211  0.192088017 -0.808745776 -0.399919948
## [406] -0.214276500 -0.711036394  2.283404562 -1.020767426 -0.544917926
## [411]  0.006109019  0.211219205 -0.964786899  1.010636449 -1.028557523
## [416]  2.202001714 -0.140940282  0.108142017 -0.919785089 -0.977452092
## [421] -0.005600916  0.474186563 -0.042202731  0.029386913 -0.650385190
## [426]  2.713938533  1.956478889  0.769672284  0.104501632  0.117255756
## [431] -0.740112539  1.915656287 -0.536046543  0.102809144 -0.801680601
## [436] -0.759753800  1.760541037 -0.771997850  0.506019753 -0.104233166
## [441] -0.541975130  1.999422833  0.896150563  0.104492616 -0.913770400
## [446] -0.920746643 -0.814087664 -1.047688710  0.105460181 -0.965303158
## [451] -0.741156728  0.635827880 -0.709795388 -1.064906265 -0.965730136
## [456]  0.037134190  0.601411438 -0.964424525  0.190711792  2.826659903
## [461] -0.599817166  1.003589877  0.762232253 -0.780967356  1.641562798
## [466] -1.026643890 -0.955221393  2.504787476 -0.877145386 -0.708227227
## [471] -0.737562916 -0.954364257  1.295032960  0.147104525 -0.886348518
## [476]  0.828746136 -0.844289504 -0.977541024 -0.716152542  1.858181219
## [481]  1.818545801  0.295813503 -0.943742080  0.618687125 -0.871315208
## [486]  0.024588903  0.168484098 -0.970730973  0.627619931 -0.346802476
## [491]  0.598958458 -1.035450844 -0.933119902 -0.476736169  0.021367562
## [496]  0.760369327 -1.003049274 -0.384373271 -0.854067028  0.858634719
## [501]  0.062617651 -0.001128184 -0.964424525 -0.743387084  0.412967328
## [506] -1.041827907  2.214952369  0.017978214  1.445664747  1.534375252
## [511] -1.047688710  1.073734558 -0.100648369  0.059201877 -1.028264174
## [516]  0.628989240 -0.201650787  0.826856211 -0.958836989  2.051681755
## [521]  0.710618450  0.620806875 -0.649575756 -0.944242677 -1.040949274
## [526] -0.150634288 -0.946082865 -0.892725581  0.398058344 -0.423827822
## [531] -0.690140229 -0.907820490 -1.055564909 -1.010701235 -0.104093527
## [536]  0.515229071  6.863676311  1.400456943 -1.024816185 -0.595529231
## [541] -0.400223903  0.951488913 -0.685036850 -1.019455804 -1.055306779
## [546]  2.377351952 -0.361777480  1.393895544  0.525150940 -0.554729254
## [551] -0.767697146 -0.886348518  1.964607033 -0.904066670  4.140273072
## [556] -0.717413457  1.496049864 -0.239887753 -1.003565532 -0.695473102
## [561]  0.113486911 -0.672774020  1.680024423  1.969285136 -0.315417761
## [566] -0.964217103 -0.773902181 -1.050739105  4.267814319 -0.038530417
## [571] -0.959908973  0.106777812 -1.070887148 -0.888689303 -0.786656305
## [576] -0.435684996 -1.031796848  0.110906488 -0.784751975 -0.083240468
## [581]  2.466630825  0.579363483 -0.958836989 -0.958836989 -0.885291934
## [586]  0.391678276  6.857299249 -0.058732173  4.591895143 -0.913988715
## [591] -0.970801588  0.060668911 -0.913503430  0.011625941 -0.486701495
## [596] -0.201522375 -0.030076997 -1.073762336 -0.938501605 -1.022180461
## [601]  0.771736622 -1.082621690 -0.991536156 -1.009337404 -0.950119142
## [606]  0.942897157 -0.916959019  0.493317750  1.377765637 -1.068319034
## [611]  0.951681199  0.721112588 -0.958995120 -0.995895167 -0.863270160
## [616]  0.152781454  0.288776122 -1.055875161 -0.154315904  2.555909698
## [621]  1.374501807  0.474767141 -0.709603452 -1.019922772 -1.017440758
## [626] -0.133206306 -0.082929597 -1.005126093  1.552283925 -0.842145536
## [631] -1.009426336 -0.856803991  0.293242383 -0.035567539  0.557088374
## [636]  0.149998204 -0.888689303  0.182436410  0.292515584  0.384432832
## [641] -1.008099402 -0.972663098 -1.018134881 -0.129741415 -0.856803991
## [646]  0.528400872 -1.003152277 -0.718431729 -0.913337412  0.085370444
## [651] -0.972438860 -0.095994593  0.932975224 -0.912581690 -0.856828781
## [656]  1.150931821 -0.987157412 -1.024511943 -0.014020532 -0.761561598
## [661]  0.741663353  1.476918676 -1.028858569 -1.022696720 -1.049049623
## [666]  2.482590756 -1.025419786 -0.361657574 -1.040949274 -1.034501597
## [671]  1.777909122  0.575960104 -1.050928035 -0.905307677  0.597246238
## [676] -0.678750309 -0.853207174 -0.698449416  1.448480112  0.249972874
## [681]  0.262235704 -0.110195557  1.991958015 -0.612122816  1.593931448
## [686] -0.830295788 -0.990206217  0.286865320 -0.952459927  0.088150689
## [691]  1.546048265 -0.442495047 -1.103167049 -1.003049274  0.610906330
## [696] -0.994346913 -0.855427766  1.678284518  1.387203810 -1.017112014
## [701] -1.047688710  2.591000816  0.141071518 -0.958409837 -0.070208481
## [706] -0.957976849 -1.019922772  1.040582830 -0.933328740  0.152449418
## [711]  0.814167311 -0.195145312
Temp2_pca$x
##                 PC1           PC2           PC3          PC4
##   [1,] -1.036571945 -0.1675817029 -0.4512155112 -0.280517248
##   [2,]  2.328844131  0.1022918285 -0.0644045317  1.147406212
##   [3,] -0.076863406 -1.0364253330  1.0155382614  0.470315955
##   [4,]  0.541154997 -0.4004517724  1.3498713191  0.005941459
##   [5,] -0.943742080  0.5783575367 -0.0185714058 -0.051183852
##   [6,] -0.278861772  1.7828311382  0.6470218066 -0.311526470
##   [7,] -0.992543997 -1.2748413981 -1.1050763987 -0.843594832
##   [8,] -0.030671121 -0.9706142289  1.0512734542  0.444011801
##   [9,]  1.664344689 -1.3812908595 -0.8941309506  1.278937145
##  [10,] -0.108260428 -2.2716456857  0.2912731112 -0.059238176
##  [11,]  0.358340114  0.8443588327  2.0935020004  0.802227620
##  [12,] -1.039398015 -0.2798683728 -0.5170560246 -0.328690272
##  [13,] -0.630009991  0.8694448494  0.1324763008 -0.301524135
##  [14,] -0.154266787 -1.7231957561  0.6166953333  0.249299556
##  [15,]  0.208282705  0.6444468869  1.9855747253  0.894059299
##  [16,] -0.121191971 -1.1120830961 -1.8628754064 -0.286066237
##  [17,]  0.080053345 -0.7233559402  1.1895595915  0.422118607
##  [18,] -0.720981351  0.6264512250 -0.0045681066 -0.301859366
##  [19,] -0.888689303  0.5344050809 -0.0479420797 -0.138812068
##  [20,]  0.625733012 -1.5243219921 -0.1140148752  0.935304605
##  [21,] -0.647725138  0.2513992845 -0.2297830451 -0.564031854
##  [22,] -0.028458129 -2.0310634439  0.4276154032 -0.046334256
##  [23,]  0.290832573 -0.2869811981  1.4326297117  0.364662359
##  [24,]  2.118171868  0.3460076983 -0.3513946758 -3.907620912
##  [25,]  0.875161156  1.1995167387 -1.3652222002  1.106508508
##  [26,] -0.715648479  2.3585887361  1.0135414535  0.488114652
##  [27,]  1.474364633  0.6588246642 -1.7215319207  0.124097704
##  [28,] -0.353680136  1.0966188162  0.2483413792 -0.535451822
##  [29,] -1.033020953 -0.2226533122 -0.4838237166 -0.310189844
##  [30,] -0.002848466 -1.4671517284  0.7575395885  0.181613043
##  [31,]  1.430674269 -1.4317399327 -0.9088200604  1.541889474
##  [32,]  0.031651073 -0.2312615472  1.4819997708  0.707675872
##  [33,]  0.091775301 -0.9441782404  1.0589707441  0.306221266
##  [34,]  1.737017034 -1.9798219080 -1.2507083116  0.914715217
##  [35,]  0.649379751 -1.2958636466  0.0187973373  1.011401099
##  [36,] -0.005330479 -1.4676875913  0.7573835629  0.184406085
##  [37,] -0.729676286 -0.9388973610 -0.9243947250 -1.011020158
##  [38,] -1.036123470 -0.2233231407 -0.4840187487 -0.306698542
##  [39,]  2.466575808  0.7462487722  0.3053993550  1.274857785
##  [40,]  0.166579768 -0.8163515486  1.1293360004  0.273396074
##  [41,]  1.459736803  2.7216822690 -0.5076885621  1.090593468
##  [42,] -0.076792792 -1.3156014023  0.8513855516  0.341853400
##  [43,]  0.547522780  0.4866401084 -1.7633798140  1.179923077
##  [44,]  0.035247891 -2.1848242042  0.3331258345 -0.195053315
##  [45,] -0.614660418 -0.6907125655 -0.7858388195 -1.037742521
##  [46,]  0.506071875  0.1147422142 -1.9793898155  1.059670295
##  [47,]  0.056057955  1.3525954097  0.3725928346 -0.919505513
##  [48,] -0.895091155 -1.1421249580 -1.0332874086 -0.901906532
##  [49,] -0.025776293 -0.8578809172  1.1172440150  0.489856824
##  [50,] -1.044431067 -0.3367932638 -0.5502038446 -0.348703132
##  [51,] -0.134256967 -1.5513608787  0.7164474901  0.303812103
##  [52,] -0.993534474  0.0650630709 -0.3171843486 -0.226241395
##  [53,] -0.932468599  0.4132766744 -0.1163570157 -0.140899900
##  [54,]  0.343048387 -1.5041496720  0.7136206745 -0.258982373
##  [55,] -0.220781974 -0.0472922039 -0.4327643331 -1.224212819
##  [56,]  0.621242869  0.3629605012 -1.8408241584  1.032773366
##  [57,] -0.361657574  0.5365138702 -0.0804744001 -0.783240892
##  [58,] -1.012476731  0.0051352047 -0.3512065362 -0.230602048
##  [59,] -0.901655367 -1.3205494547 -1.1377756838 -0.975914620
##  [60,]  0.005110655 -0.7953742112  1.1520170759  0.480775963
##  [61,] -1.014854325 -0.1628929032 -0.4498502870 -0.304956365
##  [62,] -0.964009855  0.2389521784 -0.2168340676 -0.182435974
##  [63,] -0.503768344  0.2824793282 -0.2207335593 -0.726028287
##  [64,] -0.102301041 -1.5444616449  0.7184563199  0.267851688
##  [65,]  0.066125823 -0.6146863442  1.2543469319  0.489144664
##  [66,] -0.738211213 -0.4381956715 -0.6294483843 -0.770326129
##  [67,]  3.069503611 -0.5246444689  1.1148325103 -3.147361192
##  [68,] -1.013889766 -0.0510081303 -0.3841267929 -0.254688560
##  [69,] -0.982004454  0.2350671729 -0.2179652533 -0.162186420
##  [70,] -1.041827907 -0.2803929825 -0.5172087736 -0.325955884
##  [71,] -0.214309508  1.3500617657  0.3884282861 -0.589580909
##  [72,] -0.845699534  0.0969804002 -0.3078910727 -0.392601955
##  [73,] -0.800620638  1.9493755407  0.7783798817  0.403998588
##  [74,]  1.158894058  2.9917603749 -0.3296117147  1.583195391
##  [75,]  1.209014909  0.3223447643 -1.9023696200  0.294316071
##  [76,]  0.161234875 -0.5383141877  1.2931571557  0.407793843
##  [77,] -0.727358414  0.5692361643 -0.0378004145 -0.320359794
##  [78,] -0.064471655 -0.9220734477  1.0819800975  0.507724595
##  [79,] -0.173778840 -0.0371443017 -0.4298095980 -1.277106050
##  [80,] -0.948998041  0.4655462570 -0.0845646682 -0.096622488
##  [81,] -0.932539213  0.6924527437  0.0477956940 -0.012437345
##  [82,] -0.990295149  0.1774389620 -0.2513178570 -0.178533413
##  [83,] -0.112161487 -1.3232374475  0.8491621866  0.381654248
##  [84,] -0.926524525  0.7495895684  0.0810052222  0.006470867
##  [85,] -0.321794824  1.3826941194  0.4145029188 -0.442949682
##  [86,]  1.473730145 -1.3945251058 -0.8896977450  1.506276452
##  [87,] -1.026643890 -0.1654382516 -0.4505914087 -0.291689416
##  [88,] -0.091546650 -1.3746250000  0.8176266572  0.332779489
##  [89,]  1.489723682 -1.2514764691 -0.8066137767  1.552470265
##  [90,] -1.034572211 -0.2229882265 -0.4839212327 -0.308444193
##  [91,]  0.050371589  2.7498782185  0.3968624480  1.279719438
##  [92,] -0.821294068  0.2697642906 -0.2078625945 -0.343035886
##  [93,]  3.500861199  0.8729890093 -1.7254669726 -2.259051431
##  [94,]  0.059862195 -2.3470248039  0.2361788623 -0.299781963
##  [95,] -0.220781974 -0.0472922039 -0.4327643331 -1.224212819
##  [96,]  0.856496849  0.7767001720 -1.6126312086  0.934937055
##  [97,]  0.027568597 -0.6509299197  1.2355074129  0.519695298
##  [98,]  0.036664218  1.8509526994  0.6668565633 -0.666591926
##  [99,]  0.492096651 -0.4466576443 -2.3085826307  0.818630611
## [100,] -1.025161831 -0.0534417513 -0.3848353832 -0.242003960
## [101,] -0.893312280  1.1476278804  0.3129130357  0.148833028
## [102,]  0.584492113  0.7458939120 -1.6133143950  1.253865794
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## [559,] -1.003565532  0.0628973813 -0.3178149261 -0.214953316
## [560,] -0.695473102  0.8553114675  0.1283611251 -0.227857654
## [561,]  0.113486911  0.0655979953  1.6513013259  0.743968043
## [562,] -0.672774020  1.0277269522  0.2282823357 -0.176371368
## [563,]  1.680024423 -0.8804690868  0.9946549267 -1.609438999
## [564,]  1.969285136 -0.7570720703 -0.5466473302  1.192549919
## [565,] -0.315417761  1.4399091800  0.4477352267 -0.424449254
## [566,] -0.964217103  0.2389074338 -0.2168470957 -0.182202755
## [567,] -0.773902181  1.5642761724  0.5502394628  0.194195636
## [568,] -1.050739105 -0.3381551591 -0.5506003837 -0.341604616
## [569,]  4.267814319  0.5209124195  0.0574840074 -1.034541892
## [570,] -0.038530417 -0.9723110385  1.0507793991  0.452855968
## [571,] -0.959908973  0.4631906041 -0.0852505569 -0.084344275
## [572,]  0.106777812 -2.1135427445  0.3704538149 -0.249870238
## [573,] -1.070887148 -0.4541816157 -0.6175297999 -0.370285000
## [574,] -0.888689303  0.5344050809 -0.0479420797 -0.138812068
## [575,] -0.786656305  1.4498460511  0.4837748470  0.157194780
## [576,] -0.435684996  0.2413401522 -0.2492850987 -0.828319973
## [577,] -1.031796848 -0.2782272929 -0.5165781961 -0.337243963
## [578,]  0.110906488 -0.7725330585  1.1586676678  0.361722550
## [579,] -0.784751975  0.0543006186 -0.3368911858 -0.486863646
## [580,] -0.083240468 -1.0936403936  0.9823059535  0.451815527
## [581,]  2.466630825 -0.3197741702  1.2739229903 -2.314880978
## [582,]  0.579363483 -0.4836551365 -2.3359282481  0.694751503
## [583,] -0.958836989 -0.0949605861 -0.4134974668 -0.342316776
## [584,] -0.958836989 -0.0949605861 -0.4134974668 -0.342316776
## [585,] -0.885291934  0.2280281211 -0.2283013761 -0.283856572
## [586,]  0.391678276  0.2931738592  1.7672834236  0.507945575
## [587,]  6.857299249  2.2118595583 -1.1533271141 -5.753651558
## [588,] -0.058732173  0.8252680362  0.0698939709 -1.021420270
## [589,]  4.591895143 -0.3583695147 -0.4802777633 -1.835736725
## [590,] -0.913988715 -0.0294396517 -0.3778467618 -0.367108498
## [591,] -0.970801588  0.3491623799 -0.1515981535 -0.123439913
## [592,]  0.060668911  2.7495474821  1.1936684346 -0.282778822
## [593,] -0.913503430 -0.4760409833 -0.6404676935 -0.573067542
## [594,]  0.011625941 -0.7939675713  1.1524266431  0.473444228
## [595,] -0.486701495 -0.2163803329 -0.5151435620 -0.976323397
## [596,] -0.201522375  0.4898833233 -0.9158137147  0.548952532
## [597,] -0.030076997 -2.2547660068  0.2961879182 -0.147218997
## [598,] -1.073762336 -1.0690232568 -0.9788562686 -0.649492317
## [599,] -0.938501605  0.4678124209 -0.0839048359 -0.108434262
## [600,] -1.022180461 -0.1086363412 -0.4174793966 -0.271035553
## [601,]  0.771736622  0.3752278537  1.7911748463  0.080261028
## [602,] -1.082621690 -1.3685539190 -1.1544047104 -0.776379148
## [603,] -0.991536156  0.1771710306 -0.2513958698 -0.177136892
## [604,] -1.009337404 -0.3850548604 -0.5808291985 -0.413871101
## [605,] -0.950119142  0.5211424761 -0.0518037137 -0.069684280
## [606,]  0.942897157 -0.4253928025  1.3094629815 -0.497497401
## [607,] -0.916959019  0.9191695350  0.1801008232  0.072736535
## [608,]  0.493317750  0.0003120929 -2.0458544313  1.022669439
## [609,]  1.377765637 -0.1639905980  1.4352941963 -0.909830642
## [610,] -1.068319034 -0.5094654268 -0.6501997915 -0.398851551
## [611,]  0.951681199  0.5815923917  1.9009809039 -0.045203065
## [612,]  0.721112588 -0.6382366167  0.4008680858  1.225960326
## [613,] -0.958995120  0.4075496405 -0.1180245395 -0.111049264
## [614,] -0.995895167 -0.0471231248 -0.3829956072 -0.274938114
## [615,] -0.863270160  1.3216287153  0.4132958480  0.192056100
## [616,]  0.152781454  0.7441407806  2.0477486367  1.007868808
## [617,]  0.288776122  0.6059870250  1.9578033140  0.777802403
## [618,] -1.055875161 -0.3951022883 -0.5837546788 -0.361501565
## [619,] -0.154315904 -2.2257507272  0.3212093779  0.018265263
## [620,]  2.555909698  0.4812366788  1.7391753012 -2.055874986
## [621,]  1.374501807 -1.4997057412 -0.9451826323  1.579424450
## [622,]  0.474767141 -1.4198735389  0.7547322762 -0.381530563
## [623,] -0.709603452  0.2938781176 -0.2008414417 -0.468722773
## [624,] -1.019922772  0.0035276162 -0.3516746131 -0.222222922
## [625,] -1.017440758  0.0040634791 -0.3515185874 -0.225015964
## [626,] -0.133206306 -1.4952957797  0.7493449671  0.328306399
## [627,] -0.082929597 -0.7687927323 -1.6634815589 -0.175063669
## [628,] -1.005126093 -1.3333961158 -1.1386987707 -0.855112655
## [629,]  1.552283925  1.6807360493 -1.1256679827  0.498593253
## [630,] -0.842145536 -0.4606349272 -0.6359819570 -0.653367498
## [631,] -1.009426336  0.0057937801 -0.3510147807 -0.234034697
## [632,] -0.856803991  0.8204803841  0.1182194599 -0.046309928
## [633,]  0.293242383  0.3277599687  1.7939269256  0.644393371
## [634,] -0.035567539 -0.7483183059  1.1822913721  0.552228276
## [635,]  0.557088374  0.5724626993 -1.7135313522  1.207673719
## [636,]  0.149998204 -0.7640932190  1.1611250713  0.317732140
## [637,] -0.888689303  0.5344050809 -0.0479420797 -0.138812068
## [638,]  0.182436410 -0.7012515988  1.1959956482  0.306905627
## [639,]  0.292515584 -0.4948547042 -0.7288114561 -2.058599349
## [640,]  0.384432832 -1.1165091774 -2.6955386055  0.642450851
## [641,] -1.008099402  0.1177567890 -0.2852685068 -0.184174676
## [642,] -0.972663098  0.3487604828 -0.1517151727 -0.121345131
## [643,] -1.018134881  0.7856493007  0.1080777947  0.135237798
## [644,] -0.129741415 -1.4945477152  0.7495627788  0.324407312
## [645,] -0.856803991  0.8204803841  0.1182194599 -0.046309928
## [646,]  0.528400872 -0.5148818937  1.2834067033 -0.031059397
## [647,] -1.003152277  0.0629866024 -0.3177889479 -0.215418357
## [648,] -0.718431729  0.8503547364  0.1269178881 -0.202022016
## [649,] -0.913337412  0.5849218563 -0.0166600920 -0.085398616
## [650,]  0.085370444 -2.1181645613  0.3691080939 -0.225780251
## [651,] -0.972438860  0.3208897639 -0.1681167914 -0.134435778
## [652,] -0.095994593 -1.2080705149  0.9158413376  0.414814671
## [653,]  0.932975224  0.7094543375 -1.6570707304  0.810360028
## [654,] -0.912581690  1.0317911193  0.2460388526  0.119163907
## [655,] -0.856828781 -0.7988345942 -0.8338935611 -0.790903964
## [656,]  1.150931821  0.6804485484  1.9463377286 -0.243745737
## [657,] -0.987157412  0.1222781315 -0.2839520407 -0.207740967
## [658,] -1.024511943  0.7284342401  0.0748454868  0.116737370
## [659,] -0.014020532 -0.9670193932  1.0523201521  0.425274679
## [660,] -0.761561598 -1.2249726642 -1.0905562646 -1.103522298
## [661,]  0.741663353 -1.0069974816 -2.6540399679  0.255347188
## [662,]  1.476918676 -1.3659175755 -0.8730815910  1.515526666
## [663,] -1.028858569 -1.3480124243 -1.1457719968 -0.832771220
## [664,] -1.022696720 -0.1087478006 -0.4175118499 -0.270454600
## [665,] -1.049049623 -0.3936286656 -0.5833256084 -0.369182430
## [666,]  2.482590756  0.1913237442 -0.0219082027  1.000069775
## [667,] -1.025419786 -0.2210122323 -0.4833458882 -0.318743535
## [668,] -0.361657574  0.5365138702 -0.0804744001 -0.783240892
## [669,] -1.040949274 -0.2802032871 -0.5171535406 -0.326944621
## [670,] -1.034501597 -0.5021642958 -0.6480739424 -0.436906748
## [671,]  1.777909122 -0.4633602706 -0.3616891289  1.561967520
## [672,]  0.575960104  0.8278092592 -1.5646035940  1.301981901
## [673,] -1.050928035 -0.4498724749 -0.6162751199 -0.392745247
## [674,] -0.905307677  0.9775233041  0.2136646856  0.085301749
## [675,]  0.597246238  0.8603240333 -1.5468497792  1.290866650
## [676,] -0.678750309  0.2447009992 -0.2317333654 -0.529118830
## [677,] -0.853207174 -1.1330822729 -1.0306544763 -0.949039115
## [678,] -0.698449416  2.8090080902  1.2772740678  0.674173273
## [679,]  1.448480112 -1.7070869943 -1.0718578891  1.393469238
## [680,]  0.249972874 -1.5242445278  0.7077697138 -0.154243300
## [681,]  0.262235704  0.0418743610  1.6278206191  0.550902494
## [682,] -0.110195557 -1.4903277955  0.7507914806  0.302412107
## [683,]  1.991958015  0.4711569300  1.7693867405 -1.369899663
## [684,] -0.612122816  1.5433658179  0.5275778906 -0.013533383
## [685,]  1.593931448 -0.8381103369 -0.5702430064  1.614940254
## [686,] -0.830295788  0.9378799892  0.1855486917 -0.024786714
## [687,] -0.990206217 -0.2134096785 -0.4811322747 -0.358369817
## [688,]  0.286865320  0.2705449081  1.7606946177  0.625892943
## [689,] -0.952459927 -0.0377455255 -0.3802651588 -0.323816348
## [690,]  0.088150689 -0.1073868437  1.5512143381  0.695449364
## [691,]  1.546048265 -0.6809334511 -0.4747587744  1.745853671
## [692,] -0.442495047  0.4632229249 -0.1183874766 -0.717950062
## [693,] -1.103167049 -1.1870482139 -1.0463675823 -0.667756051
## [694,] -1.003049274  0.0630088408 -0.3177824728 -0.215534269
## [695,]  0.610906330  0.2846665856  1.7482332202  0.235568806
## [696,] -0.994346913  0.4557555074 -0.0874154123 -0.045590818
## [697,] -0.855427766  1.2674836128  0.3809574109  0.157554335
## [698,]  1.678284518 -0.5965455906 -0.4336146414  1.622723132
## [699,]  1.387203810 -1.3852868731 -0.8787212930  1.616483960
## [700,] -1.017112014 -0.2750568606 -0.5156550705 -0.353768996
## [701,] -1.047688710 -0.3374965837 -0.5504086282 -0.345037265
## [702,]  2.591000816  1.1639797750  0.5430410319  1.314577051
## [703,]  0.141071518 -1.0452117911  0.9964067687  0.199394362
## [704,] -0.958409837  0.4635142652 -0.0851563174 -0.086031273
## [705,] -0.070208481 -1.2583415972  0.8846308877  0.360120609
## [706,] -0.957976849  0.1844164318 -0.2492862474 -0.214901612
## [707,] -1.019922772  0.0035276162 -0.3516746131 -0.222222922
## [708,]  1.040582830 -0.0946382622  0.7000179410  1.084707607
## [709,] -0.933328740  0.1338996565 -0.2805682351 -0.268315064
## [710,]  0.152449418 -1.3777848985  0.8001334335  0.032530955
## [711,]  0.814167311  0.4046125825 -1.8286964431  0.815673010
## [712,] -0.195145312  0.5470983840 -0.8825814068  0.567452960
plot(Temp2_pca$x,xlim=xlim,ylim=xlim)

Temp2_pca$rotation[,1]
##         Sex         Age        Fare    Embarked 
##  0.44571001  0.09242234  0.65697225 -0.60098933
Temp2_pca$rotation
##                  PC1        PC2        PC3        PC4
## Sex       0.44571001 -0.5293273 0.64187639  0.3303784
## Age       0.09242234  0.8292140 0.48163361  0.2681255
## Fare      0.65697225  0.1418393 0.04129893 -0.7392993
## Embarked -0.60098933 -0.1099922 0.59524631 -0.5219151
plot(Temp2[,-1])

Temp2_pca$x
##                 PC1           PC2           PC3          PC4
##   [1,] -1.036571945 -0.1675817029 -0.4512155112 -0.280517248
##   [2,]  2.328844131  0.1022918285 -0.0644045317  1.147406212
##   [3,] -0.076863406 -1.0364253330  1.0155382614  0.470315955
##   [4,]  0.541154997 -0.4004517724  1.3498713191  0.005941459
##   [5,] -0.943742080  0.5783575367 -0.0185714058 -0.051183852
##   [6,] -0.278861772  1.7828311382  0.6470218066 -0.311526470
##   [7,] -0.992543997 -1.2748413981 -1.1050763987 -0.843594832
##   [8,] -0.030671121 -0.9706142289  1.0512734542  0.444011801
##   [9,]  1.664344689 -1.3812908595 -0.8941309506  1.278937145
##  [10,] -0.108260428 -2.2716456857  0.2912731112 -0.059238176
##  [11,]  0.358340114  0.8443588327  2.0935020004  0.802227620
##  [12,] -1.039398015 -0.2798683728 -0.5170560246 -0.328690272
##  [13,] -0.630009991  0.8694448494  0.1324763008 -0.301524135
##  [14,] -0.154266787 -1.7231957561  0.6166953333  0.249299556
##  [15,]  0.208282705  0.6444468869  1.9855747253  0.894059299
##  [16,] -0.121191971 -1.1120830961 -1.8628754064 -0.286066237
##  [17,]  0.080053345 -0.7233559402  1.1895595915  0.422118607
##  [18,] -0.720981351  0.6264512250 -0.0045681066 -0.301859366
##  [19,] -0.888689303  0.5344050809 -0.0479420797 -0.138812068
##  [20,]  0.625733012 -1.5243219921 -0.1140148752  0.935304605
##  [21,] -0.647725138  0.2513992845 -0.2297830451 -0.564031854
##  [22,] -0.028458129 -2.0310634439  0.4276154032 -0.046334256
##  [23,]  0.290832573 -0.2869811981  1.4326297117  0.364662359
##  [24,]  2.118171868  0.3460076983 -0.3513946758 -3.907620912
##  [25,]  0.875161156  1.1995167387 -1.3652222002  1.106508508
##  [26,] -0.715648479  2.3585887361  1.0135414535  0.488114652
##  [27,]  1.474364633  0.6588246642 -1.7215319207  0.124097704
##  [28,] -0.353680136  1.0966188162  0.2483413792 -0.535451822
##  [29,] -1.033020953 -0.2226533122 -0.4838237166 -0.310189844
##  [30,] -0.002848466 -1.4671517284  0.7575395885  0.181613043
##  [31,]  1.430674269 -1.4317399327 -0.9088200604  1.541889474
##  [32,]  0.031651073 -0.2312615472  1.4819997708  0.707675872
##  [33,]  0.091775301 -0.9441782404  1.0589707441  0.306221266
##  [34,]  1.737017034 -1.9798219080 -1.2507083116  0.914715217
##  [35,]  0.649379751 -1.2958636466  0.0187973373  1.011401099
##  [36,] -0.005330479 -1.4676875913  0.7573835629  0.184406085
##  [37,] -0.729676286 -0.9388973610 -0.9243947250 -1.011020158
##  [38,] -1.036123470 -0.2233231407 -0.4840187487 -0.306698542
##  [39,]  2.466575808  0.7462487722  0.3053993550  1.274857785
##  [40,]  0.166579768 -0.8163515486  1.1293360004  0.273396074
##  [41,]  1.459736803  2.7216822690 -0.5076885621  1.090593468
##  [42,] -0.076792792 -1.3156014023  0.8513855516  0.341853400
##  [43,]  0.547522780  0.4866401084 -1.7633798140  1.179923077
##  [44,]  0.035247891 -2.1848242042  0.3331258345 -0.195053315
##  [45,] -0.614660418 -0.6907125655 -0.7858388195 -1.037742521
##  [46,]  0.506071875  0.1147422142 -1.9793898155  1.059670295
##  [47,]  0.056057955  1.3525954097  0.3725928346 -0.919505513
##  [48,] -0.895091155 -1.1421249580 -1.0332874086 -0.901906532
##  [49,] -0.025776293 -0.8578809172  1.1172440150  0.489856824
##  [50,] -1.044431067 -0.3367932638 -0.5502038446 -0.348703132
##  [51,] -0.134256967 -1.5513608787  0.7164474901  0.303812103
##  [52,] -0.993534474  0.0650630709 -0.3171843486 -0.226241395
##  [53,] -0.932468599  0.4132766744 -0.1163570157 -0.140899900
##  [54,]  0.343048387 -1.5041496720  0.7136206745 -0.258982373
##  [55,] -0.220781974 -0.0472922039 -0.4327643331 -1.224212819
##  [56,]  0.621242869  0.3629605012 -1.8408241584  1.032773366
##  [57,] -0.361657574  0.5365138702 -0.0804744001 -0.783240892
##  [58,] -1.012476731  0.0051352047 -0.3512065362 -0.230602048
##  [59,] -0.901655367 -1.3205494547 -1.1377756838 -0.975914620
##  [60,]  0.005110655 -0.7953742112  1.1520170759  0.480775963
##  [61,] -1.014854325 -0.1628929032 -0.4498502870 -0.304956365
##  [62,] -0.964009855  0.2389521784 -0.2168340676 -0.182435974
##  [63,] -0.503768344  0.2824793282 -0.2207335593 -0.726028287
##  [64,] -0.102301041 -1.5444616449  0.7184563199  0.267851688
##  [65,]  0.066125823 -0.6146863442  1.2543469319  0.489144664
##  [66,] -0.738211213 -0.4381956715 -0.6294483843 -0.770326129
##  [67,]  3.069503611 -0.5246444689  1.1148325103 -3.147361192
##  [68,] -1.013889766 -0.0510081303 -0.3841267929 -0.254688560
##  [69,] -0.982004454  0.2350671729 -0.2179652533 -0.162186420
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## [526,] -0.150634288  0.5820734632 -0.0672089460 -1.020708111
## [527,] -0.946082865  0.0194695352 -0.3470328509 -0.305315920
## [528,] -0.892725581  1.0360780218  0.2472870575  0.096819572
## [529,]  0.398058344 -0.1521547982  1.5050330526  0.295353056
## [530,] -0.423827822  0.4672531492 -0.1172140079 -0.738956530
## [531,] -0.690140229  2.5874489786  1.1464706851  0.562116364
## [532,] -0.907820490  0.3627598990 -0.1476390034 -0.194313352
## [533,] -1.055564909 -0.3950353055 -0.5837351756 -0.361850695
## [534,] -1.010701235 -0.0224006000 -0.3675106389 -0.245438346
## [535,] -0.104093527 -1.4890103767  0.7511750695  0.295545414
## [536,]  0.515229071  0.0406569652  1.6108929883  0.240529183
## [537,]  6.863676311  2.2690746189 -1.1200948062 -5.735151130
## [538,]  1.400456943  0.5870298479 -1.7590093736  0.181590361
## [539,] -1.024816185 -0.2767201788 -0.5161393741 -0.345099393
## [540,] -0.595529231 -0.5190673836 -0.6861418958 -0.982241237
## [541,] -0.400223903  2.0916588243  0.8363812565 -0.020896392
## [542,]  0.951488913  0.3784218357 -1.8528954919  0.635466626
## [543,] -0.685036850 -0.5383919366 -0.6917685696 -0.881517162
## [544,] -1.019455804 -0.3314011441 -0.5486338368 -0.376808117
## [545,] -1.055306779 -0.3949795758 -0.5837189490 -0.362141172
## [546,]  2.377351952 -1.1207850191  0.8086706795 -2.573886970
## [547,] -0.361777480  0.4806497197 -0.1133133674 -0.808782579
## [548,]  1.393895544 -1.9980630309 -1.2394463610  1.326510863
## [549,]  0.525150940  0.2863761430 -1.8796961683  1.115230232
## [550,] -0.554729254  2.0583013637  0.8266686618  0.152970469
## [551,] -0.767697146  1.5656158294  0.5506295269  0.187213031
## [552,] -0.886348518  1.0932930825  0.2805193655  0.115320000
## [553,]  1.964607033  1.9372707439 -1.0012540266  0.111630608
## [554,] -0.904066670  0.9777912355  0.2137426984  0.083905228
## [555,]  4.140273072 -0.6233887932 -0.6071621510 -1.404550452
## [556,] -0.717413457  0.6272215278 -0.0043438198 -0.305874364
## [557,]  1.496049864 -1.1942723936 -0.7733846673  1.571027950
## [558,] -0.239887753  0.1465707212 -1.1152140373  0.438065875
## [559,] -1.003565532  0.0628973813 -0.3178149261 -0.214953316
## [560,] -0.695473102  0.8553114675  0.1283611251 -0.227857654
## [561,]  0.113486911  0.0655979953  1.6513013259  0.743968043
## [562,] -0.672774020  1.0277269522  0.2282823357 -0.176371368
## [563,]  1.680024423 -0.8804690868  0.9946549267 -1.609438999
## [564,]  1.969285136 -0.7570720703 -0.5466473302  1.192549919
## [565,] -0.315417761  1.4399091800  0.4477352267 -0.424449254
## [566,] -0.964217103  0.2389074338 -0.2168470957 -0.182202755
## [567,] -0.773902181  1.5642761724  0.5502394628  0.194195636
## [568,] -1.050739105 -0.3381551591 -0.5506003837 -0.341604616
## [569,]  4.267814319  0.5209124195  0.0574840074 -1.034541892
## [570,] -0.038530417 -0.9723110385  1.0507793991  0.452855968
## [571,] -0.959908973  0.4631906041 -0.0852505569 -0.084344275
## [572,]  0.106777812 -2.1135427445  0.3704538149 -0.249870238
## [573,] -1.070887148 -0.4541816157 -0.6175297999 -0.370285000
## [574,] -0.888689303  0.5344050809 -0.0479420797 -0.138812068
## [575,] -0.786656305  1.4498460511  0.4837748470  0.157194780
## [576,] -0.435684996  0.2413401522 -0.2492850987 -0.828319973
## [577,] -1.031796848 -0.2782272929 -0.5165781961 -0.337243963
## [578,]  0.110906488 -0.7725330585  1.1586676678  0.361722550
## [579,] -0.784751975  0.0543006186 -0.3368911858 -0.486863646
## [580,] -0.083240468 -1.0936403936  0.9823059535  0.451815527
## [581,]  2.466630825 -0.3197741702  1.2739229903 -2.314880978
## [582,]  0.579363483 -0.4836551365 -2.3359282481  0.694751503
## [583,] -0.958836989 -0.0949605861 -0.4134974668 -0.342316776
## [584,] -0.958836989 -0.0949605861 -0.4134974668 -0.342316776
## [585,] -0.885291934  0.2280281211 -0.2283013761 -0.283856572
## [586,]  0.391678276  0.2931738592  1.7672834236  0.507945575
## [587,]  6.857299249  2.2118595583 -1.1533271141 -5.753651558
## [588,] -0.058732173  0.8252680362  0.0698939709 -1.021420270
## [589,]  4.591895143 -0.3583695147 -0.4802777633 -1.835736725
## [590,] -0.913988715 -0.0294396517 -0.3778467618 -0.367108498
## [591,] -0.970801588  0.3491623799 -0.1515981535 -0.123439913
## [592,]  0.060668911  2.7495474821  1.1936684346 -0.282778822
## [593,] -0.913503430 -0.4760409833 -0.6404676935 -0.573067542
## [594,]  0.011625941 -0.7939675713  1.1524266431  0.473444228
## [595,] -0.486701495 -0.2163803329 -0.5151435620 -0.976323397
## [596,] -0.201522375  0.4898833233 -0.9158137147  0.548952532
## [597,] -0.030076997 -2.2547660068  0.2961879182 -0.147218997
## [598,] -1.073762336 -1.0690232568 -0.9788562686 -0.649492317
## [599,] -0.938501605  0.4678124209 -0.0839048359 -0.108434262
## [600,] -1.022180461 -0.1086363412 -0.4174793966 -0.271035553
## [601,]  0.771736622  0.3752278537  1.7911748463  0.080261028
## [602,] -1.082621690 -1.3685539190 -1.1544047104 -0.776379148
## [603,] -0.991536156  0.1771710306 -0.2513958698 -0.177136892
## [604,] -1.009337404 -0.3850548604 -0.5808291985 -0.413871101
## [605,] -0.950119142  0.5211424761 -0.0518037137 -0.069684280
## [606,]  0.942897157 -0.4253928025  1.3094629815 -0.497497401
## [607,] -0.916959019  0.9191695350  0.1801008232  0.072736535
## [608,]  0.493317750  0.0003120929 -2.0458544313  1.022669439
## [609,]  1.377765637 -0.1639905980  1.4352941963 -0.909830642
## [610,] -1.068319034 -0.5094654268 -0.6501997915 -0.398851551
## [611,]  0.951681199  0.5815923917  1.9009809039 -0.045203065
## [612,]  0.721112588 -0.6382366167  0.4008680858  1.225960326
## [613,] -0.958995120  0.4075496405 -0.1180245395 -0.111049264
## [614,] -0.995895167 -0.0471231248 -0.3829956072 -0.274938114
## [615,] -0.863270160  1.3216287153  0.4132958480  0.192056100
## [616,]  0.152781454  0.7441407806  2.0477486367  1.007868808
## [617,]  0.288776122  0.6059870250  1.9578033140  0.777802403
## [618,] -1.055875161 -0.3951022883 -0.5837546788 -0.361501565
## [619,] -0.154315904 -2.2257507272  0.3212093779  0.018265263
## [620,]  2.555909698  0.4812366788  1.7391753012 -2.055874986
## [621,]  1.374501807 -1.4997057412 -0.9451826323  1.579424450
## [622,]  0.474767141 -1.4198735389  0.7547322762 -0.381530563
## [623,] -0.709603452  0.2938781176 -0.2008414417 -0.468722773
## [624,] -1.019922772  0.0035276162 -0.3516746131 -0.222222922
## [625,] -1.017440758  0.0040634791 -0.3515185874 -0.225015964
## [626,] -0.133206306 -1.4952957797  0.7493449671  0.328306399
## [627,] -0.082929597 -0.7687927323 -1.6634815589 -0.175063669
## [628,] -1.005126093 -1.3333961158 -1.1386987707 -0.855112655
## [629,]  1.552283925  1.6807360493 -1.1256679827  0.498593253
## [630,] -0.842145536 -0.4606349272 -0.6359819570 -0.653367498
## [631,] -1.009426336  0.0057937801 -0.3510147807 -0.234034697
## [632,] -0.856803991  0.8204803841  0.1182194599 -0.046309928
## [633,]  0.293242383  0.3277599687  1.7939269256  0.644393371
## [634,] -0.035567539 -0.7483183059  1.1822913721  0.552228276
## [635,]  0.557088374  0.5724626993 -1.7135313522  1.207673719
## [636,]  0.149998204 -0.7640932190  1.1611250713  0.317732140
## [637,] -0.888689303  0.5344050809 -0.0479420797 -0.138812068
## [638,]  0.182436410 -0.7012515988  1.1959956482  0.306905627
## [639,]  0.292515584 -0.4948547042 -0.7288114561 -2.058599349
## [640,]  0.384432832 -1.1165091774 -2.6955386055  0.642450851
## [641,] -1.008099402  0.1177567890 -0.2852685068 -0.184174676
## [642,] -0.972663098  0.3487604828 -0.1517151727 -0.121345131
## [643,] -1.018134881  0.7856493007  0.1080777947  0.135237798
## [644,] -0.129741415 -1.4945477152  0.7495627788  0.324407312
## [645,] -0.856803991  0.8204803841  0.1182194599 -0.046309928
## [646,]  0.528400872 -0.5148818937  1.2834067033 -0.031059397
## [647,] -1.003152277  0.0629866024 -0.3177889479 -0.215418357
## [648,] -0.718431729  0.8503547364  0.1269178881 -0.202022016
## [649,] -0.913337412  0.5849218563 -0.0166600920 -0.085398616
## [650,]  0.085370444 -2.1181645613  0.3691080939 -0.225780251
## [651,] -0.972438860  0.3208897639 -0.1681167914 -0.134435778
## [652,] -0.095994593 -1.2080705149  0.9158413376  0.414814671
## [653,]  0.932975224  0.7094543375 -1.6570707304  0.810360028
## [654,] -0.912581690  1.0317911193  0.2460388526  0.119163907
## [655,] -0.856828781 -0.7988345942 -0.8338935611 -0.790903964
## [656,]  1.150931821  0.6804485484  1.9463377286 -0.243745737
## [657,] -0.987157412  0.1222781315 -0.2839520407 -0.207740967
## [658,] -1.024511943  0.7284342401  0.0748454868  0.116737370
## [659,] -0.014020532 -0.9670193932  1.0523201521  0.425274679
## [660,] -0.761561598 -1.2249726642 -1.0905562646 -1.103522298
## [661,]  0.741663353 -1.0069974816 -2.6540399679  0.255347188
## [662,]  1.476918676 -1.3659175755 -0.8730815910  1.515526666
## [663,] -1.028858569 -1.3480124243 -1.1457719968 -0.832771220
## [664,] -1.022696720 -0.1087478006 -0.4175118499 -0.270454600
## [665,] -1.049049623 -0.3936286656 -0.5833256084 -0.369182430
## [666,]  2.482590756  0.1913237442 -0.0219082027  1.000069775
## [667,] -1.025419786 -0.2210122323 -0.4833458882 -0.318743535
## [668,] -0.361657574  0.5365138702 -0.0804744001 -0.783240892
## [669,] -1.040949274 -0.2802032871 -0.5171535406 -0.326944621
## [670,] -1.034501597 -0.5021642958 -0.6480739424 -0.436906748
## [671,]  1.777909122 -0.4633602706 -0.3616891289  1.561967520
## [672,]  0.575960104  0.8278092592 -1.5646035940  1.301981901
## [673,] -1.050928035 -0.4498724749 -0.6162751199 -0.392745247
## [674,] -0.905307677  0.9775233041  0.2136646856  0.085301749
## [675,]  0.597246238  0.8603240333 -1.5468497792  1.290866650
## [676,] -0.678750309  0.2447009992 -0.2317333654 -0.529118830
## [677,] -0.853207174 -1.1330822729 -1.0306544763 -0.949039115
## [678,] -0.698449416  2.8090080902  1.2772740678  0.674173273
## [679,]  1.448480112 -1.7070869943 -1.0718578891  1.393469238
## [680,]  0.249972874 -1.5242445278  0.7077697138 -0.154243300
## [681,]  0.262235704  0.0418743610  1.6278206191  0.550902494
## [682,] -0.110195557 -1.4903277955  0.7507914806  0.302412107
## [683,]  1.991958015  0.4711569300  1.7693867405 -1.369899663
## [684,] -0.612122816  1.5433658179  0.5275778906 -0.013533383
## [685,]  1.593931448 -0.8381103369 -0.5702430064  1.614940254
## [686,] -0.830295788  0.9378799892  0.1855486917 -0.024786714
## [687,] -0.990206217 -0.2134096785 -0.4811322747 -0.358369817
## [688,]  0.286865320  0.2705449081  1.7606946177  0.625892943
## [689,] -0.952459927 -0.0377455255 -0.3802651588 -0.323816348
## [690,]  0.088150689 -0.1073868437  1.5512143381  0.695449364
## [691,]  1.546048265 -0.6809334511 -0.4747587744  1.745853671
## [692,] -0.442495047  0.4632229249 -0.1183874766 -0.717950062
## [693,] -1.103167049 -1.1870482139 -1.0463675823 -0.667756051
## [694,] -1.003049274  0.0630088408 -0.3177824728 -0.215534269
## [695,]  0.610906330  0.2846665856  1.7482332202  0.235568806
## [696,] -0.994346913  0.4557555074 -0.0874154123 -0.045590818
## [697,] -0.855427766  1.2674836128  0.3809574109  0.157554335
## [698,]  1.678284518 -0.5965455906 -0.4336146414  1.622723132
## [699,]  1.387203810 -1.3852868731 -0.8787212930  1.616483960
## [700,] -1.017112014 -0.2750568606 -0.5156550705 -0.353768996
## [701,] -1.047688710 -0.3374965837 -0.5504086282 -0.345037265
## [702,]  2.591000816  1.1639797750  0.5430410319  1.314577051
## [703,]  0.141071518 -1.0452117911  0.9964067687  0.199394362
## [704,] -0.958409837  0.4635142652 -0.0851563174 -0.086031273
## [705,] -0.070208481 -1.2583415972  0.8846308877  0.360120609
## [706,] -0.957976849  0.1844164318 -0.2492862474 -0.214901612
## [707,] -1.019922772  0.0035276162 -0.3516746131 -0.222222922
## [708,]  1.040582830 -0.0946382622  0.7000179410  1.084707607
## [709,] -0.933328740  0.1338996565 -0.2805682351 -0.268315064
## [710,]  0.152449418 -1.3777848985  0.8001334335  0.032530955
## [711,]  0.814167311  0.4046125825 -1.8286964431  0.815673010
## [712,] -0.195145312  0.5470983840 -0.8825814068  0.567452960
plot(Temp2_pca)

#get the original value of the data based on PCA
center <- Temp2_pca$center
scale <- Temp2_pca$scale
new_tita <- as.matrix(Temp2[,-1])
new_tita
##        Sex   Age     Fare Embarked
##   [1,]   1 22.00   7.2500        3
##   [2,]   2 38.00  71.2833        1
##   [3,]   2 26.00   7.9250        3
##   [4,]   2 35.00  53.1000        3
##   [5,]   1 35.00   8.0500        3
##   [6,]   1 54.00  51.8625        3
##   [7,]   1  2.00  21.0750        3
##   [8,]   2 27.00  11.1333        3
##   [9,]   2 14.00  30.0708        1
##  [10,]   2  4.00  16.7000        3
##  [11,]   2 58.00  26.5500        3
##  [12,]   1 20.00   8.0500        3
##  [13,]   1 39.00  31.2750        3
##  [14,]   2 14.00   7.8542        3
##  [15,]   2 55.00  16.0000        3
##  [16,]   1  2.00  29.1250        2
##  [17,]   2 31.00  18.0000        3
##  [18,]   1 35.00  26.0000        3
##  [19,]   1 34.00  13.0000        3
##  [20,]   2 15.00   8.0292        2
##  [21,]   1 28.00  35.5000        3
##  [22,]   2  8.00  21.0750        3
##  [23,]   2 38.00  31.3875        3
##  [24,]   1 19.00 263.0000        3
##  [25,]   1 40.00  27.7208        1
##  [26,]   1 66.00  10.5000        3
##  [27,]   1 28.00  82.1708        1
##  [28,]   1 42.00  52.0000        3
##  [29,]   1 21.00   8.0500        3
##  [30,]   2 18.00  18.0000        3
##  [31,]   2 14.00  11.2417        1
##  [32,]   2 40.00   9.4750        3
##  [33,]   2 27.00  21.0000        3
##  [34,]   2  3.00  41.5792        1
##  [35,]   2 19.00   7.8792        2
##  [36,]   2 18.00  17.8000        3
##  [37,]   1  7.00  39.6875        3
##  [38,]   1 21.00   7.8000        3
##  [39,]   2 49.00  76.7292        1
##  [40,]   2 29.00  26.0000        3
##  [41,]   1 65.00  61.9792        1
##  [42,]   2 21.00  10.5000        3
##  [43,]   1 28.50   7.2292        1
##  [44,]   2  5.00  27.7500        3
##  [45,]   1 11.00  46.9000        3
##  [46,]   1 22.00   7.2292        1
##  [47,]   1 45.00  83.4750        3
##  [48,]   1  4.00  27.9000        3
##  [49,]   2 29.00  10.5000        3
##  [50,]   1 19.00   8.1583        3
##  [51,]   2 17.00   7.9250        3
##  [52,]   1 26.00   8.6625        3
##  [53,]   1 32.00  10.5000        3
##  [54,]   2 16.00  46.9000        3
##  [55,]   1 21.00  73.5000        3
##  [56,]   1 26.00  14.4542        1
##  [57,]   1 32.00  56.4958        3
##  [58,]   1 25.00   7.6500        3
##  [59,]   1  0.83  29.0000        3
##  [60,]   2 30.00  12.4750        3
##  [61,]   1 22.00   9.0000        3
##  [62,]   1 29.00   9.5000        3
##  [63,]   1 28.00  47.1000        3
##  [64,]   2 17.00  10.5000        3
##  [65,]   2 33.00  15.8500        3
##  [66,]   1 16.00  34.3750        3
##  [67,]   2 23.00 263.0000        3
##  [68,]   1 24.00   8.0500        3
##  [69,]   1 29.00   8.0500        3
##  [70,]   1 20.00   7.8542        3
##  [71,]   1 46.00  61.1750        3
##  [72,]   1 26.00  20.5750        3
##  [73,]   1 59.00   7.2500        3
##  [74,]   1 71.00  34.6542        1
##  [75,]   1 23.00  63.3583        1
##  [76,]   2 34.00  23.0000        3
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##  [82,]   1 28.00   7.8958        3
##  [83,]   2 21.00   7.6500        3
##  [84,]   1 38.00   7.8958        3
##  [85,]   1 47.00  52.0000        3
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##  [90,]   1 21.00   7.9250        3
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##  [95,]   1 21.00  73.5000        3
##  [96,]   1 32.50  30.0708        1
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##  [99,]   1 12.00  11.2417        1
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## [101,]   1 45.00   6.9750        3
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## [109,]   1 37.00  53.1000        3
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## [119,]   1 36.50  26.0000        3
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## [139,]   1 21.00   7.9250        3
## [140,]   1 56.00  30.6958        1
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## [150,]   1 36.00   7.8958        3
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## [158,]   2 24.00  13.0000        3
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## [160,]   1 34.00   6.4958        3
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## [174,]   1 42.00  27.0000        3
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## [189,]   1 24.00  10.5000        3
## [190,]   1 44.00  26.0000        3
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## [197,]   1 44.00  90.0000        2
## [198,]   2 25.00   7.7750        3
## [199,]   2 24.00  14.5000        3
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## [201,]   1 54.00  26.0000        3
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## [208,]   2 35.00 512.3292        1
## [209,]   2 50.00  26.0000        3
## [210,]   1  3.00  31.3875        3
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## [212,]   1 40.00   0.0000        3
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## [219,]   2 41.00  19.5000        3
## [220,]   1 37.00  29.7000        1
## [221,]   2 63.00  77.9583        3
## [222,]   2 45.00   7.7500        3
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## [224,]   2 35.00  20.2500        3
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## [226,]   1 28.00   7.8542        3
## [227,]   1 16.00   9.5000        3
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## [230,]   1 30.00   9.5000        3
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## [250,]   1 28.00   7.8958        3
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## [256,]   2 40.00 134.5000        1
## [257,]   1 22.00   7.2500        3
## [258,]   1 27.00   7.8958        3
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## [261,]   2 36.00 135.6333        1
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## [264,]   2 31.00  20.5250        3
## [265,]   2 16.00  57.9792        1
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## [310,]   2 36.00  13.0000        3
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## [351,]   1 64.00 263.0000        3
## [352,]   1 31.00  10.5000        3
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## [367,]   2 50.00  10.5000        3
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## [392,]   1 55.00  30.5000        3
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## [401,]   2 16.00  86.5000        3
## [402,]   1 18.00 108.9000        1
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## [411,]   2 34.00  10.5000        3
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## [415,]   1 22.00   7.8958        3
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## [511,]   1 19.00   7.8958        3
## [512,]   1 56.00  35.5000        1
## [513,]   2 23.00   7.5500        3
## [514,]   2 18.00  23.0000        3
## [515,]   1 21.00   8.4333        3
## [516,]   2 18.00   6.7500        2
## [517,]   1 24.00  73.5000        3
## [518,]   2 32.00  15.5000        2
## [519,]   1 23.00  13.0000        3
## [520,]   1 58.00 113.2750        1
## [521,]   1 50.00 133.6500        3
## [522,]   1 40.00   7.2250        1
## [523,]   1 47.00  25.5875        3
## [524,]   1 36.00   7.4958        3
## [525,]   1 20.00   7.9250        3
## [526,]   1 32.00  73.5000        3
## [527,]   1 25.00  13.0000        3
## [528,]   1 43.00   8.0500        3
## [529,]   2 40.00  39.0000        3
## [530,]   1 31.00  52.0000        3
## [531,]   1 70.00  10.5000        3
## [532,]   1 31.00  13.0000        3
## [533,]   1 18.00   7.7750        3
## [534,]   1 24.50   8.0500        3
## [535,]   2 18.00   9.8417        3
## [536,]   2 43.00  46.9000        3
## [537,]   1 36.00 512.3292        1
## [538,]   1 27.00  76.7292        1
## [539,]   1 20.00   9.2250        3
## [540,]   1 14.00  46.9000        3
## [541,]   1 60.00  39.0000        3
## [542,]   1 25.00  41.5792        1
## [543,]   1 14.00  39.6875        3
## [544,]   1 19.00  10.1708        3
## [545,]   1 18.00   7.7958        3
## [546,]   2 15.00 211.3375        3
## [547,]   1 31.00  57.0000        3
## [548,]   2  4.00  13.4167        1
## [549,]   1 25.00   7.2250        1
## [550,]   1 60.00  26.5500        3
## [551,]   1 52.00  13.5000        3
## [552,]   1 44.00   8.0500        3
## [553,]   1 49.00 110.8833        1
## [554,]   1 42.00   7.6500        3
## [555,]   2 18.00 227.5250        1
## [556,]   1 35.00  26.2875        3
## [557,]   2 18.00  14.4542        1
## [558,]   1 25.00   7.7417        2
## [559,]   1 26.00   7.8542        3
## [560,]   1 39.00  26.0000        3
## [561,]   2 45.00  13.5000        3
## [562,]   1 42.00  26.2875        3
## [563,]   2 22.00 151.5500        3
## [564,]   2 24.00  49.5042        1
## [565,]   1 48.00  52.0000        3
## [566,]   1 29.00   9.4833        3
## [567,]   1 52.00  13.0000        3
## [568,]   1 19.00   7.6500        3
## [569,]   2 38.00 227.5250        1
## [570,]   2 27.00  10.5000        3
## [571,]   1 33.00   7.7750        3
## [572,]   2  6.00  33.0000        3
## [573,]   1 17.00   7.0542        3
## [574,]   1 34.00  13.0000        3
## [575,]   1 50.00  13.0000        3
## [576,]   1 27.00  53.1000        3
## [577,]   1 20.00   8.6625        3
## [578,]   2 30.00  21.0000        3
## [579,]   1 25.00  26.0000        3
## [580,]   2 25.00   7.9250        3
## [581,]   2 29.00 211.3375        3
## [582,]   1 11.00  18.7875        1
## [583,]   1 23.00  13.0000        3
## [584,]   1 23.00  13.0000        3
## [585,]   1 28.50  16.1000        3
## [586,]   2 48.00  34.3750        3
## [587,]   1 35.00 512.3292        1
## [588,]   1 36.00  78.8500        3
## [589,]   2 21.00 262.3750        1
## [590,]   1 24.00  16.1000        3
## [591,]   1 31.00   7.9250        3
## [592,]   1 70.00  71.0000        3
## [593,]   1 16.00  20.2500        3
## [594,]   2 30.00  13.0000        3
## [595,]   1 19.00  53.1000        3
## [596,]   1 31.00   7.7500        2
## [597,]   2  4.00  23.0000        3
## [598,]   1  6.00  12.4750        3
## [599,]   1 33.00   9.5000        3
## [600,]   1 23.00   7.8958        3
## [601,]   2 48.00  65.0000        3
## [602,]   1  0.67  14.5000        3
## [603,]   1 28.00   7.7958        3
## [604,]   1 18.00  11.5000        3
## [605,]   1 34.00   8.0500        3
## [606,]   2 33.00  86.5000        3
## [607,]   1 41.00   7.1250        3
## [608,]   1 20.00   7.2292        1
## [609,]   2 36.00 120.0000        3
## [610,]   1 16.00   7.7750        3
## [611,]   2 51.00  77.9583        3
## [612,]   2 30.50   7.7500        2
## [613,]   1 32.00   8.3625        3
## [614,]   1 24.00   9.5000        3
## [615,]   1 48.00   7.8542        3
## [616,]   2 57.00  10.5000        3
## [617,]   2 54.00  23.0000        3
## [618,]   1 18.00   7.7500        3
## [619,]   2  5.00  12.4750        3
## [620,]   2 43.00 211.3375        3
## [621,]   2 13.00   7.2292        1
## [622,]   2 17.00  57.0000        3
## [623,]   1 29.00  30.0000        3
## [624,]   1 25.00   7.0500        3
## [625,]   1 25.00   7.2500        3
## [626,]   2 18.00   7.4958        3
## [627,]   1  8.00  29.1250        2
## [628,]   1  1.00  20.5750        3
## [629,]   1 46.00  79.2000        1
## [630,]   1 16.00  26.0000        3
## [631,]   1 25.00   7.8958        3
## [632,]   1 39.00  13.0000        3
## [633,]   2 49.00  25.9292        3
## [634,]   2 31.00   8.6833        3
## [635,]   1 30.00   7.2292        1
## [636,]   2 30.00  24.1500        3
## [637,]   1 34.00  13.0000        3
## [638,]   2 31.00  26.2500        3
## [639,]   1 11.00 120.0000        3
## [640,]   1  0.42   8.5167        1
## [641,]   1 27.00   6.9750        3
## [642,]   1 31.00   7.7750        3
## [643,]   1 39.00   0.0000        3
## [644,]   2 18.00   7.7750        3
## [645,]   1 39.00  13.0000        3
## [646,]   2 33.00  53.1000        3
## [647,]   1 26.00   7.8875        3
## [648,]   1 39.00  24.1500        3
## [649,]   1 35.00  10.5000        3
## [650,]   2  6.00  31.2750        3
## [651,]   1 30.50   8.0500        3
## [652,]   2 23.00   7.9250        3
## [653,]   1 31.00  37.0042        1
## [654,]   1 43.00   6.4500        3
## [655,]   1 10.00  27.9000        3
## [656,]   2 52.00  93.5000        3
## [657,]   1 27.00   8.6625        3
## [658,]   1 38.00   0.0000        3
## [659,]   2 27.00  12.4750        3
## [660,]   1  2.00  39.6875        3
## [661,]   1  1.00  37.0042        1
## [662,]   2 15.00  14.4542        1
## [663,]   1  0.83  18.7500        3
## [664,]   1 23.00   7.8542        3
## [665,]   1 18.00   8.3000        3
## [666,]   2 39.00  83.1583        1
## [667,]   1 21.00   8.6625        3
## [668,]   1 32.00  56.4958        3
## [669,]   1 20.00   7.9250        3
## [670,]   1 16.00  10.5000        3
## [671,]   2 30.00  31.0000        1
## [672,]   1 34.50   6.4375        1
## [673,]   1 17.00   8.6625        3
## [674,]   1 42.00   7.5500        3
## [675,]   1 35.00   7.8958        1
## [676,]   1 28.00  33.0000        3
## [677,]   1  4.00  31.2750        3
## [678,]   1 74.00   7.7750        3
## [679,]   2  9.00  15.2458        1
## [680,]   2 16.00  39.4000        3
## [681,]   2 44.00  26.0000        3
## [682,]   2 18.00   9.3500        3
## [683,]   2 45.00 164.8667        3
## [684,]   1 51.00  26.5500        3
## [685,]   2 24.00  19.2583        1
## [686,]   1 41.00  14.1083        3
## [687,]   1 21.00  11.5000        3
## [688,]   2 48.00  25.9292        3
## [689,]   1 24.00  13.0000        3
## [690,]   2 42.00  13.0000        3
## [691,]   2 27.00  13.8583        1
## [692,]   1 31.00  50.4958        3
## [693,]   1  4.00  11.1333        3
## [694,]   1 26.00   7.8958        3
## [695,]   2 47.00  52.5542        3
## [696,]   1 33.00   5.0000        3
## [697,]   1 47.00   9.0000        3
## [698,]   2 28.00  24.0000        1
## [699,]   2 15.00   7.2250        1
## [700,]   1 20.00   9.8458        3
## [701,]   1 19.00   7.8958        3
## [702,]   2 56.00  83.1583        1
## [703,]   2 25.00  26.0000        3
## [704,]   1 33.00   7.8958        3
## [705,]   2 22.00  10.5167        3
## [706,]   1 28.00  10.5000        3
## [707,]   1 25.00   7.0500        3
## [708,]   2 39.00  29.1250        2
## [709,]   1 27.00  13.0000        3
## [710,]   2 19.00  30.0000        3
## [711,]   1 26.00  30.0000        1
## [712,]   1 32.00   7.7500        2
#drop(scale(new_tita,center=center, scale=scale)%*%Temp2_pca$rotation[,1])
predict(Temp2_pca)[,1]
##   [1] -1.036571945  2.328844131 -0.076863406  0.541154997 -0.943742080
##   [6] -0.278861772 -0.992543997 -0.030671121  1.664344689 -0.108260428
##  [11]  0.358340114 -1.039398015 -0.630009991 -0.154266787  0.208282705
##  [16] -0.121191971  0.080053345 -0.720981351 -0.888689303  0.625733012
##  [21] -0.647725138 -0.028458129  0.290832573  2.118171868  0.875161156
##  [26] -0.715648479  1.474364633 -0.353680136 -1.033020953 -0.002848466
##  [31]  1.430674269  0.031651073  0.091775301  1.737017034  0.649379751
##  [36] -0.005330479 -0.729676286 -1.036123470  2.466575808  0.166579768
##  [41]  1.459736803 -0.076792792  0.547522780  0.035247891 -0.614660418
##  [46]  0.506071875  0.056057955 -0.895091155 -0.025776293 -1.044431067
##  [51] -0.134256967 -0.993534474 -0.932468599  0.343048387 -0.220781974
##  [56]  0.621242869 -0.361657574 -1.012476731 -0.901655367  0.005110655
##  [61] -1.014854325 -0.964009855 -0.503768344 -0.102301041  0.066125823
##  [66] -0.738211213  3.069503611 -1.013889766 -0.982004454 -1.041827907
##  [71] -0.214309508 -0.845699534 -0.800620638  1.158894058  1.209014909
##  [76]  0.161234875 -0.727358414 -0.064471655 -0.173778840 -0.948998041
##  [81] -0.932539213 -0.990295149 -0.112161487 -0.926524525 -0.321794824
##  [86]  1.473730145 -1.026643890 -0.091546650  1.489723682 -1.034572211
##  [91]  0.050371589 -0.821294068  3.500861199  0.059862195 -0.220781974
##  [96]  0.856496849  0.027568597  0.036664218  0.492096651 -1.025161831
## [101] -0.893312280  0.584492113 -1.051808084  0.138651104  0.166579768
## [106] -0.946082865  0.609453478  0.106324917 -0.371914372 -1.050427438
## [111]  1.411988553 -0.104543417  0.008732262 -0.290457192 -1.009337404
## [116] -0.689606114 -0.997913218  0.142972844 -0.711415758 -0.837672804
## [121] -0.786174026  0.625789110 -0.813012301 -0.828623295  1.363011889
## [126]  0.628437935 -0.975627392 -0.786447467  0.109524253 -1.004548410
## [131] -1.050928035 -0.767938660 -0.954730098  0.292191896 -0.387165823
## [136] -0.462102217 -0.108437846 -0.196474743 -1.034572211  1.014114107
## [141] -1.054582031  1.877062338 -0.914197553 -1.037266068 -0.819925729
## [146] -0.776470582 -0.042176813 -0.650385190 -0.047950783 -0.939278650
## [151]  0.024380066 -0.984345239 -0.122381475 -0.925047347  1.826492899
## [156]  3.390087901 -0.894706997 -0.026636433 -0.970386917 -0.969406870
## [161]  0.655880718 -1.052152140 -0.198422354 -0.866074733  0.675019418
## [166]  0.628645183  0.915856252 -1.026299834  0.142791800 -1.036571945
## [171] -0.914197553  2.805324565 -0.070486344 -0.663931846  2.352736343
## [176] -0.945222724 -1.064906265 -0.933328740 -0.841709082  0.092394215
## [181] -1.010510802 -1.015370410 -1.046137539 -0.990722301  0.918110825
## [186] -0.985417223 -0.723057710  0.080389515 -0.983485098 -0.663587790
## [191]  0.035763975 -1.015370410 -0.904063665 -0.951599786 -1.038123204
## [196]  0.557036252  0.902107564 -0.085101979 -0.008021331 -0.378687788
## [201] -0.599817166 -0.026241670 -0.541975130 -0.875726341  0.171281245
## [206]  1.576021360  0.923765970  7.783122743  0.300498078 -0.858188104
## [211]  0.053228880 -1.011757819 -0.906960350 -0.672282725 -1.010925472
## [216]  1.933332924  1.565398897 -1.107413754  0.162439072  0.880591976
## [221]  1.028205947  0.042129017 -0.089306659  0.133484249  0.015297746
## [226] -0.990811408 -1.046911665 -1.045775078  0.594006912 -0.957632792
## [231] -1.028557523 -0.837672804  0.666907557  0.803320697  2.453348419
## [236]  0.665415513 -0.078138217 -1.015803398  0.515637469  1.552483175
## [241]  4.592488314 -1.145676128  0.619772454  2.661751642  0.765215150
## [246]  2.099692269  2.386934820  4.572763956  0.147448581 -0.990295149
## [251] -0.666862335 -0.077742039  0.134694456 -0.748737987  1.902679142
## [256]  3.126121828 -1.036571945 -0.996672211  0.775010371  0.159170537
## [261]  3.114677909 -0.800431707  0.049888315  0.111388768  2.023443967
## [266] -0.622997025  0.879968183 -0.941426084 -0.255394947  3.132498891
## [271] -0.879971456 -0.539315078 -0.931424410  3.075880674 -0.926951678
## [276] -0.946082865 -0.875935179 -0.026636433  0.075396564 -1.050389038
## [281] -0.891501476 -1.005684998  0.461432438 -0.886514536 -0.970386917
## [286]  0.481832316  0.062642440 -0.665516910  0.805013470  1.668230548
## [291] -0.956152148 -0.985555446  2.518366521  2.214952369  1.123523486
## [296] -1.071439868 -1.045775078  2.099575543 -0.060343441 -0.110748452
## [301]  3.072971793  0.453398283 -1.049187846  4.293322569  1.403617766
## [306] -0.964424525  0.527503921 -0.239913161 -0.678431042  0.049888315
## [311]  1.459216011  0.451942143 -1.036175592 -0.989932775  2.754308066
## [316]  0.019280820 -1.029798530 -0.045856727 -0.650833665 -0.989862160
## [321] -0.005471708 -0.919785089 -1.001135641 -0.085169588 -0.891582983
## [326] -0.105973355 -0.789408756 -0.845432102 -1.015020343 -1.036433722
## [331]  1.757783372 -0.887899777  0.279130525 -0.064898808 -0.914197553
## [336]  0.022456956 -0.265500247 -0.984176216  0.016245912 -0.901214683
## [341]  0.160202706  0.102809144 -0.962873267 -0.758795250  0.249481579
## [346] -1.070008516 -0.254264370  1.237470265  0.219497592  0.044721460
## [351]  2.405139675 -0.938845662  0.271715283 -1.021403416 -1.010925472
## [356] -0.001128184 -0.225464960 -0.016118675 -0.720532876  1.472767262
## [361] -0.556725983 -0.692886669  0.811752906  1.694326912  0.558983863
## [366] -0.522843943  0.108142017 -0.631254003 -0.950119142 -0.489330748
## [371] -0.799410430 -0.937020961 -0.580237504  1.445664747 -0.917009726
## [376]  0.213805637  1.519713505 -0.078637400 -0.789408756 -0.994466645
## [381] -1.033211299 -0.175773979 -0.627414543 -0.848086144  0.179719640
## [386]  1.565787300  0.999086522  1.014510286 -0.975627392 -1.012126664
## [391] -1.042949008 -0.537594796  1.343183574 -1.033020953  2.517541600
## [396]  1.699155610 -1.017044405 -1.050928035  0.660530495  0.013916019
## [401]  0.834487097  1.742305211  0.192088017 -0.808745776 -0.399919948
## [406] -0.214276500 -0.711036394  2.283404562 -1.020767426 -0.544917926
## [411]  0.006109019  0.211219205 -0.964786899  1.010636449 -1.028557523
## [416]  2.202001714 -0.140940282  0.108142017 -0.919785089 -0.977452092
## [421] -0.005600916  0.474186563 -0.042202731  0.029386913 -0.650385190
## [426]  2.713938533  1.956478889  0.769672284  0.104501632  0.117255756
## [431] -0.740112539  1.915656287 -0.536046543  0.102809144 -0.801680601
## [436] -0.759753800  1.760541037 -0.771997850  0.506019753 -0.104233166
## [441] -0.541975130  1.999422833  0.896150563  0.104492616 -0.913770400
## [446] -0.920746643 -0.814087664 -1.047688710  0.105460181 -0.965303158
## [451] -0.741156728  0.635827880 -0.709795388 -1.064906265 -0.965730136
## [456]  0.037134190  0.601411438 -0.964424525  0.190711792  2.826659903
## [461] -0.599817166  1.003589877  0.762232253 -0.780967356  1.641562798
## [466] -1.026643890 -0.955221393  2.504787476 -0.877145386 -0.708227227
## [471] -0.737562916 -0.954364257  1.295032960  0.147104525 -0.886348518
## [476]  0.828746136 -0.844289504 -0.977541024 -0.716152542  1.858181219
## [481]  1.818545801  0.295813503 -0.943742080  0.618687125 -0.871315208
## [486]  0.024588903  0.168484098 -0.970730973  0.627619931 -0.346802476
## [491]  0.598958458 -1.035450844 -0.933119902 -0.476736169  0.021367562
## [496]  0.760369327 -1.003049274 -0.384373271 -0.854067028  0.858634719
## [501]  0.062617651 -0.001128184 -0.964424525 -0.743387084  0.412967328
## [506] -1.041827907  2.214952369  0.017978214  1.445664747  1.534375252
## [511] -1.047688710  1.073734558 -0.100648369  0.059201877 -1.028264174
## [516]  0.628989240 -0.201650787  0.826856211 -0.958836989  2.051681755
## [521]  0.710618450  0.620806875 -0.649575756 -0.944242677 -1.040949274
## [526] -0.150634288 -0.946082865 -0.892725581  0.398058344 -0.423827822
## [531] -0.690140229 -0.907820490 -1.055564909 -1.010701235 -0.104093527
## [536]  0.515229071  6.863676311  1.400456943 -1.024816185 -0.595529231
## [541] -0.400223903  0.951488913 -0.685036850 -1.019455804 -1.055306779
## [546]  2.377351952 -0.361777480  1.393895544  0.525150940 -0.554729254
## [551] -0.767697146 -0.886348518  1.964607033 -0.904066670  4.140273072
## [556] -0.717413457  1.496049864 -0.239887753 -1.003565532 -0.695473102
## [561]  0.113486911 -0.672774020  1.680024423  1.969285136 -0.315417761
## [566] -0.964217103 -0.773902181 -1.050739105  4.267814319 -0.038530417
## [571] -0.959908973  0.106777812 -1.070887148 -0.888689303 -0.786656305
## [576] -0.435684996 -1.031796848  0.110906488 -0.784751975 -0.083240468
## [581]  2.466630825  0.579363483 -0.958836989 -0.958836989 -0.885291934
## [586]  0.391678276  6.857299249 -0.058732173  4.591895143 -0.913988715
## [591] -0.970801588  0.060668911 -0.913503430  0.011625941 -0.486701495
## [596] -0.201522375 -0.030076997 -1.073762336 -0.938501605 -1.022180461
## [601]  0.771736622 -1.082621690 -0.991536156 -1.009337404 -0.950119142
## [606]  0.942897157 -0.916959019  0.493317750  1.377765637 -1.068319034
## [611]  0.951681199  0.721112588 -0.958995120 -0.995895167 -0.863270160
## [616]  0.152781454  0.288776122 -1.055875161 -0.154315904  2.555909698
## [621]  1.374501807  0.474767141 -0.709603452 -1.019922772 -1.017440758
## [626] -0.133206306 -0.082929597 -1.005126093  1.552283925 -0.842145536
## [631] -1.009426336 -0.856803991  0.293242383 -0.035567539  0.557088374
## [636]  0.149998204 -0.888689303  0.182436410  0.292515584  0.384432832
## [641] -1.008099402 -0.972663098 -1.018134881 -0.129741415 -0.856803991
## [646]  0.528400872 -1.003152277 -0.718431729 -0.913337412  0.085370444
## [651] -0.972438860 -0.095994593  0.932975224 -0.912581690 -0.856828781
## [656]  1.150931821 -0.987157412 -1.024511943 -0.014020532 -0.761561598
## [661]  0.741663353  1.476918676 -1.028858569 -1.022696720 -1.049049623
## [666]  2.482590756 -1.025419786 -0.361657574 -1.040949274 -1.034501597
## [671]  1.777909122  0.575960104 -1.050928035 -0.905307677  0.597246238
## [676] -0.678750309 -0.853207174 -0.698449416  1.448480112  0.249972874
## [681]  0.262235704 -0.110195557  1.991958015 -0.612122816  1.593931448
## [686] -0.830295788 -0.990206217  0.286865320 -0.952459927  0.088150689
## [691]  1.546048265 -0.442495047 -1.103167049 -1.003049274  0.610906330
## [696] -0.994346913 -0.855427766  1.678284518  1.387203810 -1.017112014
## [701] -1.047688710  2.591000816  0.141071518 -0.958409837 -0.070208481
## [706] -0.957976849 -1.019922772  1.040582830 -0.933328740  0.152449418
## [711]  0.814167311 -0.195145312
#The aboved two gives us the same thing. predict is a good function to know.
Temp2$Survived <- as.factor(Temp2$Survived)
out <- sapply(1:4, function(i){plot(Temp2$Survived,Temp2_pca$x[,i],xlab=paste("PC",i,sep=""),ylab="Survived")})

pairs(Temp2_pca$x[,1:4], ylim = c(-6,4),xlim = c(-6,4),panel=function(x,y,...){text(x,y,Temp2$Survived)})

# Better Ways to Visualize

library(factoextra)
## Warning: package 'factoextra' was built under R version 4.2.2
## Loading required package: ggplot2
## Warning: package 'ggplot2' was built under R version 4.2.2
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa

library(FactoMineR)
## Warning: package 'FactoMineR' was built under R version 4.2.2
library(ggfortify)
## Warning: package 'ggfortify' was built under R version 4.2.2
library(psych)
## Warning: package 'psych' was built under R version 4.2.2
## 
## Attaching package: 'psych'
## 
## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha
## 
## The following object is masked from 'package:car':
## 
##     logit
library(corrplot)
## Warning: package 'corrplot' was built under R version 4.2.2
## corrplot 0.92 loaded
library(devtools)
## Warning: package 'devtools' was built under R version 4.2.2
## Loading required package: usethis
## Warning: package 'usethis' was built under R version 4.2.2
# Correlation
pairs.panels(Temp2[,-1],
             gap = 0,
             bg = c("red", "blue")[Temp2$Survived],
             pch=21)

pairs.panels(Temp2_pca$x,
             gap=0,
             bg = c("red", "blue")[Temp2$Survived],
             pch=21)

fviz_eig(Temp2_pca, addlabels = TRUE)

fviz_pca_var(Temp2_pca,col.var = "cos2",
             gradient.cols = c("#FFCC00", "#CC9933", "#660033", "#330033"),
             repel = TRUE)

fviz_pca_ind(Temp2_pca, col.ind = "cos2", 
                  gradient.cols = c("#FFCC00", "#CC9933", "#660033", "#330033"), 
                  repel = TRUE)

biplot(Temp2_pca)

autoplot(Temp2_pca,
         data = Temp2[,-1],
         loadings = TRUE,
         labels = Temp2$Survived)

# Different PCA Method. 
res.pca <- PCA(Temp2[,-1], graph = FALSE)
print(res.pca)
## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 712 individuals, described by 4 variables
## *The results are available in the following objects:
## 
##    name               description                          
## 1  "$eig"             "eigenvalues"                        
## 2  "$var"             "results for the variables"          
## 3  "$var$coord"       "coord. for the variables"           
## 4  "$var$cor"         "correlations variables - dimensions"
## 5  "$var$cos2"        "cos2 for the variables"             
## 6  "$var$contrib"     "contributions of the variables"     
## 7  "$ind"             "results for the individuals"        
## 8  "$ind$coord"       "coord. for the individuals"         
## 9  "$ind$cos2"        "cos2 for the individuals"           
## 10 "$ind$contrib"     "contributions of the individuals"   
## 11 "$call"            "summary statistics"                 
## 12 "$call$centre"     "mean of the variables"              
## 13 "$call$ecart.type" "standard error of the variables"    
## 14 "$call$row.w"      "weights for the individuals"        
## 15 "$call$col.w"      "weights for the variables"
# Visualize and Interpret PCA using these functions 

#get_eigenvalue(res.pca): Extract the eigenvalues/variances of principal components
#fviz_eig(res.pca): Visualize the eigenvalues
#get_pca_ind(res.pca), get_pca_var(res.pca): Extract the results for individuals and variables, respectively.
#fviz_pca_ind(res.pca), fviz_pca_var(res.pca): Visualize the results individuals and variables, respectively.
#fviz_pca_biplot(res.pca): Make a biplot of individuals and variables.

eig.val <- get_eigenvalue(res.pca)
eig.val
##       eigenvalue variance.percent cumulative.variance.percent
## Dim.1  1.3962390         34.90598                    34.90598
## Dim.2  1.0834721         27.08680                    61.99278
## Dim.3  0.8357525         20.89381                    82.88659
## Dim.4  0.6845364         17.11341                   100.00000
fviz_eig(res.pca, addlabels = TRUE, ylim = c(0, 50))

var <- get_pca_var(res.pca)
#var$coord: coordinates of variables to create a scatter plot
#var$cos2: represents the quality of representation for variables on the factor map. It’s calculated as the squared coordinates: var.cos2 = var.coord * var.coord.
#var$contrib: contains the contributions (in percentage) of the variables to the principal components. 
#The contribution of a variable (var) to a given principal component is (in percentage) : (var.cos2 * 100) / (total cos2 of the component).
var
## Principal Component Analysis Results for variables
##  ===================================================
##   Name       Description                                    
## 1 "$coord"   "Coordinates for the variables"                
## 2 "$cor"     "Correlations between variables and dimensions"
## 3 "$cos2"    "Cos2 for the variables"                       
## 4 "$contrib" "contributions of the variables"
# Coordinates
head(var$coord)
##               Dim.1      Dim.2      Dim.3      Dim.4
## Sex       0.5266623 -0.5509767 0.58680018 -0.2733442
## Age       0.1092086  0.8631286 0.44030704 -0.2218382
## Fare      0.7762952  0.1476404 0.03775527  0.6116720
## Embarked -0.7101444 -0.1144908 0.54417120  0.4318154
# Cos2: quality on the factore map
head(var$cos2)
##               Dim.1      Dim.2       Dim.3      Dim.4
## Sex      0.27737322 0.30357527 0.344334452 0.07471705
## Age      0.01192652 0.74499101 0.193870285 0.04921218
## Fare     0.60263426 0.02179770 0.001425461 0.37414258
## Embarked 0.50430502 0.01310815 0.296122294 0.18646454
# Contributions to the principal components
head(var$contrib)
##               Dim.1     Dim.2      Dim.3     Dim.4
## Sex      19.8657409 28.018743 41.2005295 10.914987
## Age       0.8541888 68.759592 23.1970933  7.189126
## Fare     43.1612532  2.011838  0.1705601 54.656349
## Embarked 36.1188170  1.209828 35.4318171 27.239538
#The plot Below is also known as variable correlation plots. It shows the relationships between all variables. It can be interpreted as follow:

#Positively correlated variables are grouped together.
#Negatively correlated variables are positioned on opposite sides of the plot origin (opposed quadrants).
#The distance between variables and the origin measures the quality of the variables on the factor map. 
#Variables that are away from the origin are well represented on the factor map.

# Correlation circle
fviz_pca_var(res.pca, col.var = "black")

# Quality of representation


corrplot(var$cos2, is.corr=FALSE)

# Total cos2 of variables on Dim.1 and Dim.2
#A high cos2 indicates a good representation of the variable on the principal component. 
#In this case the variable is positioned close to the circumference of the correlation circle.
#A low cos2 indicates that the variable is not perfectly represented by the PCs. 
#In this case the variable is close to the center of the circle.

fviz_cos2(res.pca, choice = "var", axes = 1:2)

fviz_pca_var(res.pca, col.var = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"), 
             repel = TRUE # Avoid text overlapping
             )

# Change the transparency by cos2 values
fviz_pca_var(res.pca, alpha.var = "cos2")

corrplot(var$contrib, is.corr=FALSE)

# Contributions of variables to PC1
fviz_contrib(res.pca, choice = "var", axes = 1, top = 10)

# Contributions of variables to PC2
fviz_contrib(res.pca, choice = "var", axes = 2, top = 10)

fviz_pca_var(res.pca, col.var = "contrib",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07")
             )

fviz_pca_var(res.pca, alpha.var = "contrib")

fviz_pca_ind(res.pca,
             geom.ind = "point", # show points only (nbut not "text")
             col.ind = Temp2$Survived, # color by groups
             palette = c("#00AFBB", "#E7B800", "#FC4E07"),
             addEllipses = TRUE, # Concentration ellipses
             legend.title = "Groups"
             )

# Graph of Indiviuals
ind <- get_pca_ind(res.pca)
ind
## Principal Component Analysis Results for individuals
##  ===================================================
##   Name       Description                       
## 1 "$coord"   "Coordinates for the individuals" 
## 2 "$cos2"    "Cos2 for the individuals"        
## 3 "$contrib" "contributions of the individuals"
## Principal Component Analysis Results for individuals
##  ===================================================
##   Name       Description                       
## 1 "$coord"   "Coordinates for the individuals" 
## 2 "$cos2"    "Cos2 for the individuals"        
## 3 "$contrib" "contributions of the individuals"
#To get access to the different components, use this:

# Coordinates of individuals
head(ind$coord)
##         Dim.1      Dim.2       Dim.3        Dim.4
## 1 -1.03730064 -0.1676995 -0.45153271  0.280714448
## 2  2.33048128  0.1023637 -0.06444981 -1.148212825
## 3 -0.07691744 -1.0371539  1.01625217 -0.470646581
## 4  0.54153542 -0.4007333  1.35082026 -0.005945636
## 5 -0.94440552  0.5787641 -0.01858446  0.051219834
## 6 -0.27905781  1.7840844  0.64747666  0.311745469
# Quality of individuals
head(ind$cos2)
##         Dim.1       Dim.2        Dim.3        Dim.4
## 1 0.775882656 0.020279178 0.1470161970 5.682197e-02
## 2 0.802928484 0.001549094 0.0006140855 1.949083e-01
## 3 0.002532788 0.460506403 0.4421322704 9.482854e-02
## 4 0.128702188 0.070476288 0.8008060097 1.551418e-05
## 5 0.725218601 0.272367380 0.0002808354 2.133184e-03
## 6 0.020616435 0.842667072 0.1109873388 2.572915e-02
# Contributions of individuals
head(ind$contrib)
##          Dim.1       Dim.2        Dim.3        Dim.4
## 1 0.1082354509 0.003645573 3.426264e-02 1.616788e-02
## 2 0.5463255028 0.001358296 6.980485e-04 2.705006e-01
## 3 0.0005951273 0.139440423 1.735583e-01 4.544785e-02
## 4 0.0294994538 0.020816758 3.066461e-01 7.253040e-06
## 5 0.0897175219 0.043421563 5.804199e-05 5.382696e-04
## 6 0.0078333692 0.412603659 7.045155e-02 1.993994e-02
fviz_pca_ind(res.pca)

fviz_pca_ind(res.pca, col.ind = "cos2", 
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE # Avoid text overlapping (slow if many points)
             )

fviz_pca_ind(res.pca, pointsize = "cos2", 
             pointshape = 21, fill = "#E7B800",
             repel = TRUE # Avoid text overlapping (slow if many points)
             )

fviz_pca_ind(res.pca, col.ind = "cos2", pointsize = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE # Avoid text overlapping (slow if many points)
             )

fviz_cos2(res.pca, choice = "ind")

# Total contribution on PC1 and PC2
fviz_contrib(res.pca, choice = "ind", axes = 1:2)

# Create a random continuous variable of length 23,
# Same length as the number of active individuals in the PCA
set.seed(123)
my.cont.var <- rnorm(49)
# Color individuals by the continuous variable


fviz_pca_ind(res.pca,
             geom.ind = "point", # show points only (nbut not "text")
             col.ind = Temp2$Survived, # color by groups
             palette = c("#00AFBB", "#E7B800", "#FC4E07"),
             addEllipses = TRUE, # Concentration ellipses
             legend.title = "Groups"
             )

fviz_pca_ind(res.pca, geom.ind = "point", col.ind = Temp2$Survived, 
             palette = c("#00AFBB", "#E7B800", "#FC4E07"),
             addEllipses = TRUE, ellipse.type = "confidence",
             legend.title = "Groups"
             )

fviz_pca_ind(res.pca,
             label = "none", # hide individual labels
             habillage = Temp2$Survived, # color by groups
             addEllipses = TRUE, # Concentration ellipses
             palette = "jco"
             )

fviz_pca_var(res.pca, geom.var = c("point", "text"))

# Show individuals text labels only
fviz_pca_ind(res.pca, geom.ind =  "text")

# Change the size of arrows an labels
fviz_pca_var(res.pca, arrowsize = 1, labelsize = 5, 
             repel = TRUE)

# Change points size, shape and fill color
# Change labelsize
fviz_pca_ind(res.pca, 
             pointsize = 3, pointshape = 21, fill = "lightblue",
             labelsize = 5, repel = TRUE)

fviz_pca_ind(res.pca,
             geom.ind = "point", # show points only (but not "text")
             group.ind = Temp2$Survived, # color by groups
             legend.title = "Groups",
             mean.point = FALSE)

fviz_pca_ind(res.pca,
             geom.ind = "point", # show points only (but not "text")
             group.ind = Temp2$Survived, # color by groups
             legend.title = "Groups",
             mean.point = TRUE)

fviz_pca_var(res.pca, axes.linetype = "blank")

ind.p <- fviz_pca_ind(res.pca, geom = "point", col.ind = Temp2$Survived)
ggpubr::ggpar(ind.p,
              title = "Principal Component Analysis",
              subtitle = "Iris data set",
              caption = "Source: factoextra",
              xlab = "PC1", ylab = "PC2",
              legend.title = "Survived", legend.position = "top",
              ggtheme = theme_gray(), palette = "jco"
              )

fviz_pca_biplot(res.pca, repel = TRUE,col.ind = Temp2$Survived,
                col.var = "#2E9FDF", # Variables color
                )

fviz_pca_biplot(res.pca, 
                col.ind = Temp2$Survived, palette = "jco", 
                addEllipses = TRUE, label = "var",
                col.var = "black", repel = TRUE,
                legend.title = "Survived") 

fviz_pca_biplot(res.pca, 
                # Fill individuals by groups
                geom.ind = "point",
                pointshape = 21,
                pointsize = 2.5,
                fill.ind = Temp2$Survived,
                col.ind = "black",
                # Color variable by groups
                legend.title = list(fill = "Survived", color = "Clusters"),
                repel = TRUE        # Avoid label overplotting
             )+
  ggpubr::fill_palette("jco")+      # Indiviual fill color
  ggpubr::color_palette("npg")      # Variable colors

fviz_pca_biplot(res.pca, 
                # Individuals
                geom.ind = "point",
                fill.ind = Temp2$Survived, col.ind = "black",
                pointshape = 21, pointsize = 2,
                palette = "jco",
                addEllipses = TRUE,
                # Variables
                alpha.var ="contrib", col.var = "contrib",
                gradient.cols = "RdYlBu",
                
                legend.title = list(fill = "Survived", color = "Contrib",
                                    alpha = "Contrib")
                )

## http://www.sthda.com/english/articles/31-principal-component-methods-in-r-practical-guide/112-pca-principal-component-analysis-essentials/

# ANOVA
Temp2
## # A tibble: 712 × 5
##    Survived   Sex   Age  Fare Embarked
##    <fct>    <dbl> <dbl> <dbl>    <dbl>
##  1 0            1    22  7.25        3
##  2 1            2    38 71.3         1
##  3 1            2    26  7.92        3
##  4 1            2    35 53.1         3
##  5 0            1    35  8.05        3
##  6 0            1    54 51.9         3
##  7 0            1     2 21.1         3
##  8 1            2    27 11.1         3
##  9 1            2    14 30.1         1
## 10 1            2     4 16.7         3
## # … with 702 more rows
summary(aov(Sex ~ Age))
##              Df Sum Sq Mean Sq F value  Pr(>F)   
## Age           1   1.62  1.6163   7.033 0.00818 **
## Residuals   710 163.17  0.2298                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(aov(Age ~ Fare))
##              Df Sum Sq Mean Sq F value Pr(>F)  
## Fare          1   1296  1295.6   6.214 0.0129 *
## Residuals   710 148046   208.5                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(aov(Fare ~ Embarked))
##              Df  Sum Sq Mean Sq F value   Pr(>F)    
## Embarked      1  160160  160160   62.06 1.25e-14 ***
## Residuals   710 1832418    2581                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(aov(Sex ~ Embarked))
##              Df Sum Sq Mean Sq F value Pr(>F)   
## Embarked      1   1.98  1.9808   8.639 0.0034 **
## Residuals   710 162.80  0.2293                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# BoxM

library(biotools)
## Warning: package 'biotools' was built under R version 4.2.2
## Loading required package: MASS
## 
## Attaching package: 'MASS'
## 
## The following object is masked from 'package:dplyr':
## 
##     select
## 
## ---
## biotools version 4.2
boxM(Temp2[,2:5],Survived)
## 
##  Box's M-test for Homogeneity of Covariance Matrices
## 
## data:  Temp2[, 2:5]
## Chi-Sq (approx.) = 282.92, df = 10, p-value < 2.2e-16
# MANOVA
summary(manova(as.matrix(Temp2[,-1])~ Survived))
##            Df  Pillai approx F num Df den Df    Pr(>F)    
## Survived    1 0.32642   85.653      4    707 < 2.2e-16 ***
## Residuals 710                                             
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1